This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov. It contains both original papers and surveys, written by some distinguished experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work. Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform.

During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student—or even an established mathematician who is not an expert in the area—to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincaré and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of correlations, and measure-theoretic entropy). Smooth ergodic theory also provides a foundation for numerous applications throughout mathematics (e.g., Riemannian geometry, number theory, Lie groups, and partial differential equations), as well as other sciences. This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.

"This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms." "The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems." "The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises."--BOOK JACKET

Anatole Katok, Jean-marie Strelcyn, With The Collaboration Of Ledrappier, F. And Przytycki, F. Bibliography: P. [279]-283.

Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular ''chaotic'' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory—Cantor sets, Hausdorff dimension, box dimension—using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science—the FitzHugh-Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008. This book is published in cooperation with Mathematics Advanced Study Semesters. \"Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These...

The Theory Of Dynamical Systems Is A Major Mathematical Discipline Closely Intertwined With All Main Areas Of Mathematics. It Has Greatly Stimulated Research In Many Sciences And Given Rise To The Vast New Area Variously Called Applied Dynamics, Nonlinear Science, Or Chaos Theory. This Introduction For Senior Undergraduate And Beginning Graduate Students Of Mathematics, Physics, And Engineering Combines Mathematical Rigor With Copious Examples Of Important Applications. It Covers The Central Topological And Probabilistic Notions In Dynamics Ranging From Newtonian Mechanics To Coding Theory. Readers Need Not Be Familiar With Manifolds Or Measure Theory; The Only Prerequisite Is A Basic Undergraduate Analysis Course. The Authors Begin By Describing The Wide Array Of Scientific And Mathematical Questions That Dynamics Can Address. They Then Use A Progression Of Examples To Present The Concepts And Tools For Describing Asymptotic Behavior In Dynamical Systems, Gradually Increasing The Level Of Complexity. The Final Chapters Introduce Modern Developments And Applications Of Dynamics. Subjects Include Contractions, Logistic Maps, Equidistribution, Symbolic Dynamics, Mechanics, Hyperbolic Dynamics, Strange Attractors, Twist Maps, And Kam-theory.--pub. Desc. Pt. 1 A Course In Dynamics: From Simple To Complicated Behavior -- 2 Systems With Stable Asymptotic Behavior -- 3 Linear Maps And Linear Differential Equations -- 4 Recurrence And Equidistribution On The Circle -- 5 Recurrence And Equidistribution In Higher Dimension -- 6 Conservative Systems -- 7 Simple Systems With Complicated Orbit Structure -- 8 Entropy And Chaos -- Pt. 2 Panorama Of Dynamical Systems -- 9 Simple Dynamics As A Tool -- 10 Hyperbolic Dynamics -- 11 Quadratic Maps -- 12 Homoclinic Tangles -- 13 Strange Attractors -- 14 Variational Methods, Twist Maps, And Closed Geodesics -- 15 Dynamics, Number Theory, And Diophantine Approximatin. Boris Hasselblatt, Anatole Katok. Includes Bibliographical References And Index.

This Book Provided The First Self-contained Comprehensive Exposition Of The Theory Of Dynamical Systems As A Core Mathematical Discipline Closely Intertwined With Most Of The Main Areas Of Mathematics. The Authors Introduce And Rigorously Develop The Theory While Providing Researchers Interested In Applications With Fundamental Tools And Paradigms. The Book Begins With A Discussion Of Several Elementary But Fundamental Examples. These Are Used To Formulate A Program For The General Study Of Asymptotic Properties And To Introduce The Principal Theoretical Concepts And Methods. The Main Theme Of The Second Part Of The Book Is The Interplay Between Local Analysis Near Individual Orbits And The Global Complexity Of The Orbit Structure. The Third And Fourth Parts Develop The Theories Of Low-dimensional Dynamical Systems And Hyperbolic Dynamical Systems In Depth. Over 400 Systematic Exercises Are Included In The Text. The Book Is Aimed At Students And Researchers In Mathematics At All Levels From Advanced Undergraduate Up. Anatole Katok, Boris Hasselblatt. Includes Bibliographical References And Index.

"This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems"-- "In a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"--

<p>Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular ''chaotic'' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory—Cantor sets, Hausdorff dimension, box dimension—using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science—the FitzHugh-Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008. This book is published in cooperation with Mathematics Advanced Study Semesters.</p>

Book by Katok, Anatole, Strelcyn, Jean-Marie

This Book Provided The First Self-contained Comprehensive Exposition Of The Theory Of Dynamical Systems As A Core Mathematical Discipline Closely Intertwined With Most Of The Main Areas Of Mathematics. The Authors Introduce And Rigorously Develop The Theory While Providing Researchers Interested In Applications With Fundamental Tools And Paradigms. The Book Begins With A Discussion Of Several Elementary But Fundamental Examples. These Are Used To Formulate A Program For The General Study Of Asymptotic Properties And To Introduce The Principal Theoretical Concepts And Methods. The Main Theme Of The Second Part Of The Book Is The Interplay Between Local Analysis Near Individual Orbits And The Global Complexity Of The Orbit Structure. The Third And Fourth Parts Develop The Theories Of Low-dimensional Dynamical Systems And Hyperbolic Dynamical Systems In Depth. Over 400 Systematic Exercises Are Included In The Text. The Book Is Aimed At Students And Researchers In Mathematics At All Levels From Advanced Undergraduate Up. Anatole Katok, Boris Hasselblatt. Includes Bibliographical References And Index.

This volume presents a wide cross section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines who look for a sample of current developments in ergodic theory and dynamical systems. (Midwest) Presenting a wide cross-section of current research in the theory of dynamical systems, this collection consists of articles by leading researchers (and several Fields medallists) in a variety of specialties. Surveys featuring new results, as well as research papers, are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, and applications. The target audience is dynamicists, as well as mathematicians from other disciplines.

v. ; 24 cm "This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems"-- "In a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"-- v. 1. Introduction and cocycle problem -- v. 1. Introduction and cocycle problem

"This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms." "The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems." "The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises."--BOOK JACKET

This Book Provided The First Self-contained Comprehensive Exposition Of The Theory Of Dynamical Systems As A Core Mathematical Discipline Closely Intertwined With Most Of The Main Areas Of Mathematics. The Authors Introduce And Rigorously Develop The Theory While Providing Researchers Interested In Applications With Fundamental Tools And Paradigms. The Book Begins With A Discussion Of Several Elementary But Fundamental Examples. These Are Used To Formulate A Program For The General Study Of Asymptotic Properties And To Introduce The Principal Theoretical Concepts And Methods. The Main Theme Of The Second Part Of The Book Is The Interplay Between Local Analysis Near Individual Orbits And The Global Complexity Of The Orbit Structure. The Third And Fourth Parts Develop The Theories Of Low-dimensional Dynamical Systems And Hyperbolic Dynamical Systems In Depth. Over 400 Systematic Exercises Are Included In The Text. The Book Is Aimed At Students And Researchers In Mathematics At All Levels From Advanced Undergraduate Up. Anatole Katok, Boris Hasselblatt. Includes Bibliographical References And Index.

ОАО «РАСКАТ». – 94 с. Настоящее Руководство по эксплуатации предназначено для операторов, механиков и других лиц, связанных с эксплуатацией дорожных катков, служит для изучения конструкции катка в целом, его составных частей и специфичных требований по эксплуатации катка. Настоящее РЭ содержит все возможные варианты модификаций катков ДУ-98, ДУ-99 и ДУ- 100. Комплектацию определяет заказчик при покупке катка. Катки предназначены для уплотнения покрытий из асфальтобетонных и битумоминеральных смесей при больших объемах работ на автомобильных дорогах общего пользования. Катки пригодны для работы на открытом воздухе в условиях умеренного (исполнение У1) или тропического климата (исполнение Т1), при этом нижнее значение температуры окружающего воздуха не должно превышать минус 10°С. Описание и работа Использование по назначению Техническое обслуживание Текущий ремонт Хранение Транспортирование Утилизация Приложения «Рекомендованные масла для применения на катках" «Возможные причины появления дефекта при уплотнении дорожного покрытия» Перечень документов на которые даны ссылки в РЭ «Руководство по эксплуатации дизеля Д-243» «Руководство по эксплуатации на насос двухсекционный M4PV-65-65-K-3-35-A-R-3-B-R-V-Y1+ M4PV-50-45-N-1-35-A-R-6-B-R-V-Y1 «Руководство по эксплуатации на редуктор планетарный серии 600 типоразмер 606 W2V с адаптером для гидромотора 303.3.56.0.00 «Руководство по эксплуатации на насос аксиально – плунжерный регулируемый НП-90»... «Руководство по эксплуатации на гидромотор аксиально – поршневой нерегулируемый типа 310

The Theory Of Dynamical Systems Is A Major Mathematical Discipline Closely Intertwined With All Main Areas Of Mathematics. It Has Greatly Stimulated Research In Many Sciences And Given Rise To The Vast New Area Variously Called Applied Dynamics, Nonlinear Science, Or Chaos Theory. This Introduction For Senior Undergraduate And Beginning Graduate Students Of Mathematics, Physics, And Engineering Combines Mathematical Rigor With Copious Examples Of Important Applications. It Covers The Central Topological And Probabilistic Notions In Dynamics Ranging From Newtonian Mechanics To Coding Theory. Readers Need Not Be Familiar With Manifolds Or Measure Theory; The Only Prerequisite Is A Basic Undergraduate Analysis Course. The Authors Begin By Describing The Wide Array Of Scientific And Mathematical Questions That Dynamics Can Address. They Then Use A Progression Of Examples To Present The Concepts And Tools For Describing Asymptotic Behavior In Dynamical Systems, Gradually Increasing The Level Of Complexity. The Final Chapters Introduce Modern Developments And Applications Of Dynamics. Subjects Include Contractions, Logistic Maps, Equidistribution, Symbolic Dynamics, Mechanics, Hyperbolic Dynamics, Strange Attractors, Twist Maps, And Kam-theory.--pub. Desc. Pt. 1 A Course In Dynamics: From Simple To Complicated Behavior -- 2 Systems With Stable Asymptotic Behavior -- 3 Linear Maps And Linear Differential Equations -- 4 Recurrence And Equidistribution On The Circle -- 5 Recurrence And Equidistribution In Higher Dimension -- 6 Conservative Systems -- 7 Simple Systems With Complicated Orbit Structure -- 8 Entropy And Chaos -- Pt. 2 Panorama Of Dynamical Systems -- 9 Simple Dynamics As A Tool -- 10 Hyperbolic Dynamics -- 11 Quadratic Maps -- 12 Homoclinic Tangles -- 13 Strange Attractors -- 14 Variational Methods, Twist Maps, And Closed Geodesics -- 15 Dynamics, Number Theory, And Diophantine Approximatin. Boris Hasselblatt, Anatole Katok. Includes Bibliographical References And Index.

1 (p1): 第1章 基本概念与例子 1 (p1-1): 第1讲 1 (p1-1-1): a.三股绳索:分形、动力学与混沌 2 (p1-1-2): b.分形:错综复杂的几何学与自相似性 6 (p1-1-3): c.动力学:运动(或不动)的事物 9 (p1-2): 第2讲 9 (p1-2-1): a.动力系统:术语与记号 12 (p1-2-2): b.种群模型与logistic映射 17 (p1-3): 第3讲 17 (p1-3-1): a.具有混沌性态的线性映射与Cantor三分集 22 (p1-3-2): b.Cantor集与符号动力学 26 (p1-4): 第4讲 26 (p1-4-1): a.一些点集拓扑知识 28 (p1-4-2): b.度量空间 31 (p1-4-3): c.Lebesgue测度 34 (p1-5): 第5讲 34 (p1-5-1): a.符号空间与Cantor集的拓扑结构 37 (p1-5-2): b.编码映射没有做的事 39 (p1-5-3): c.Cantor集的几何 42 (p1-6): 第6讲 42 (p1-6-1): a.更一般的构造 46 (p1-6-2): b.它使一切有意义 49 (p2): 第2章 维数理论基础 49 (p2-1): 第7讲 49 (p2-1-1): a.Hausdorff维数的定义 54 (p2-1-2): b.Cantor三分集的Hausdorff维数 56 (p2-1-3): c.Hausdorff维数的其他定义 58 (p2-2): 第8讲 58 (p2-2-1): a.Hausdorff维数的性质 62 (p2-2-2): b.拓扑维数 63 (p2-3): 第9讲 63 (p2-3-1): a.Hausdorff维数与拓扑维数的比较 66 (p2-3-2): b.度量与拓扑 69 (p2-3-3): c.拓扑与维数 70 (p2-4): 第10讲 70 (p2-4-1): a.Cantor集的Hausdorff维数 71 (p2-4-2): b.Moran定理 76 (p2-4-3): c.Moran构造 77 (p2-4-4): d.动力学构造与叠函数系 79 (p2-5): 第11讲 79 (p2-5-1): a.盒维数:测量维数的另一个方法 82 (p2-5-2): b.盒维数的性质 85 (p2-6): 第12讲 85 (p2-6-1): a.各种不同维数之间的关系 89 (p2-6-2): b.一个反例 93 (p2-6-3): c.稳定性与次可加性 95 (p3): 第3章 测度:定义与例子 95 (p3-1): 第13讲 95 (p3-1-1): a.一点测度理论 98 (p3-1-2): b.Lebesgue测度与外测度 102 (p3-1-3): c.Hausdorff测度 103 (p3-2): 第14讲 103 (p3-2-1): a.选择一个“好”的外测度 104 (p3-2-2): b.符号空间上的Bernoulli测度 106 (p3-2-3): c.Cantor集上的测度 107 (p3-2-4): d.Markov测度 110 (p3-3): 第15讲 110 (p3-3-1): a.测度的支集 113 (p3-3-2): b.有限型子移位:一维Markov映射 115 (p4): 第4章 测度与维数 115 (p4-1): 第16讲 115 (p4-1-1): a.一致质量分布原理:用测度确定维数 117 (p4-1-2): b.点态维数和非一致质量分布原理 120 (p4-2): 第17讲 120 (p4-2-1): a.可变的点态维数 127 (p4-2-2): b.正合维数测度的Hausdorff维数 129 (p4-2-3): c.Hausdorff测度的点态维数 130 (p4-3): 第18讲 130 (p4-3-1): a.局部熵 134 (p4-3-2): b.Kolmogorov-Sinai熵 135 (p4-3-3): c.拓扑熵 138 (p4-4): 第19讲 138 (p4-4-1): a.Markov测度的熵 141 (p4-4-2): b.Markov构造的Hausdorff维数 143 (p4-5): 第20讲 143 (p4-5-1): a.Lyapunov指数 147 (p4-5-2): b.分形中的分形 151 (p5): 第5章 离散时间系统:FitzHugh-Nagumo模型 151 (p5-1): 第21讲 151 (p5-1-1): a.FitzHugh-Nagumo神经元模型 155 (p5-1-2): b.数值研究:从连续到离散 158 (p5-2): 第22讲 158 (p5-2-1): a.研究局部映射 160 (p5-2-2): b.一般映射不动点的稳定性 165 (p5-3): 第23讲 165 (p5-3-1): a.FitzHugh-Nagumo模型不动点的稳定性 167 (p5-3-2): b.周期点 171 (p5-4): 第24讲 171 (p5-4-1): a.越过倍周期:掉入兔穴 174 (p5-4-2): b.成为一维映射 179 (p6): 第6章 Logistic映射的分支图 179 (p6-1): 第25讲 179 (p6-1-1): a.Logistic映射的分支 182 (p6-1-2): b.分支的分类 185 (p6-2): 第26讲 185 (p6-2-1): a.倍周期级联 186 (p6-2-2): b.在分支图末端的混沌 189 (p6-2-3): c.中心不能把持:跑向无穷远 191 (p6-3): 第27讲 191 (p6-3-1): a.寻找相空间的有关部分:ω极限集 193 (p6-3-2): b.分支图中的稳定性窗口 194 (p6-3-3): c.稳定性窗口外的混沌 197 (p7): 第7章 混沌吸引子与持久性混沌 197 (p7-1): 第28讲 197 (p7-1-1): a.捕获区域 200 (p7-1-2): b.吸引子 203 (p7-2): 第29讲 203 (p7-2-1): a.Smale-Williams螺线管 206 (p7-2-2): b.一致双曲性 208 (p7-2-3): c.符号动力学 212 (p7-3): 第30讲 212 (p7-3-1): a.直积的维数 215 (p7-3-2): b.量化吸引子 216 (p7-3-3): c.高维中的Lyapunov指数 218 (p7-3-4): d.非共形情形 219 (p7-3-5): e.FitzHugh-Nagumo映射的吸引子 221 (p8): 第8章 马蹄与间歇性混沌 221 (p8-1): 第31讲 221 (p8-1-1): a.Smale马蹄:不是捕获区域 225 (p8-1-2): b.马蹄的Hausdorff维数 226 (p8-1-3): c.Smale马蹄上的符号动力学 229 (p8-2): 第32讲 229 (p8-2-1): a.主题的变更:其他马蹄 233 (p8-2-2): b.间歇性混沌与持久性混沌 234 (p8-2-3): c.同宿轨道与马蹄 239 (p9): 第9章 连续时间系统:Lorenz模型 239 (p9-1): 第33讲 239 (p9-1-1): a.连续时间系统:基本概念 242 (p9-1-2): b.连续时间系统的不动点 244 (p9-2): 第34讲 244 (p9-2-1): a.摆 248 (p9-2-2): b.二维系统 251 (p9-3): 第35讲 251 (p9-3-1): a.Lorenz方程 253 (p9-3-2): b.超出了线性思维 253 (p9-3-3): c.研究Lorenz系统 258 (p9-4): 第36讲 258 (p9-4-1): a.通向Poincaré映射 261 (p9-4-2): b.Lorenz系统中的马蹄 264 (p9-5): 第37讲 264 (p9-5-1): a.Lorenz吸引子 265 (p9-5-2): b.几何Lorenz吸引子 268 (p9-5-3): c.几何Lorenz吸引子的维数 269 (p9-5-4): d.回到和离开Lorenz吸引子 273 (p10): 附录 279 (p11): 部分练习提示 283 (p12): 建议阅读 289 (p13): 参考文献 293 (p14): 索引

The Theory Of Dynamical Systems Is A Major Mathematical Discipline Closely Intertwined With All Main Areas Of Mathematics. It Has Greatly Stimulated Research In Many Sciences And Given Rise To The Vast New Area Variously Called Applied Dynamics, Nonlinear Science, Or Chaos Theory. This Introduction For Senior Undergraduate And Beginning Graduate Students Of Mathematics, Physics, And Engineering Combines Mathematical Rigor With Copious Examples Of Important Applications. It Covers The Central Topological And Probabilistic Notions In Dynamics Ranging From Newtonian Mechanics To Coding Theory. Readers Need Not Be Familiar With Manifolds Or Measure Theory; The Only Prerequisite Is A Basic Undergraduate Analysis Course. The Authors Begin By Describing The Wide Array Of Scientific And Mathematical Questions That Dynamics Can Address. They Then Use A Progression Of Examples To Present The Concepts And Tools For Describing Asymptotic Behavior In Dynamical Systems, Gradually Increasing The Level Of Complexity. The Final Chapters Introduce Modern Developments And Applications Of Dynamics. Subjects Include Contractions, Logistic Maps, Equidistribution, Symbolic Dynamics, Mechanics, Hyperbolic Dynamics, Strange Attractors, Twist Maps, And Kam-theory.--pub. Desc. Pt. 1 A Course In Dynamics: From Simple To Complicated Behavior -- 2 Systems With Stable Asymptotic Behavior -- 3 Linear Maps And Linear Differential Equations -- 4 Recurrence And Equidistribution On The Circle -- 5 Recurrence And Equidistribution In Higher Dimension -- 6 Conservative Systems -- 7 Simple Systems With Complicated Orbit Structure -- 8 Entropy And Chaos -- Pt. 2 Panorama Of Dynamical Systems -- 9 Simple Dynamics As A Tool -- 10 Hyperbolic Dynamics -- 11 Quadratic Maps -- 12 Homoclinic Tangles -- 13 Strange Attractors -- 14 Variational Methods, Twist Maps, And Closed Geodesics -- 15 Dynamics, Number Theory, And Diophantine Approximatin. Boris Hasselblatt, Anatole Katok. Includes Bibliographical References And Index.

3 (p1): 第3部分 低维现象 3 (p1-1): 第10章 导言:什么是低维动力学? 9 (p1-2): 第11章 圆周同胚 9 (p1-2-1): 11.1.旋转数 15 (p1-2-2): 11.2.Poincaré分类 23 (p1-3): 第12章 圆周微分同胚 23 (p1-3-1): 12.1.Denjoy定理 25 (p1-3-2): 12.2.Denjoy例子 27 (p1-3-3): 12.3.Diophantus旋转数的局部解析共轭 32 (p1-3-4): 12.4.共轭的不变测度与正则性 34 (p1-3-5): 12.5. 奇异共轭的一个例子 37 (p1-3-6): 12.6.最速逼近法 41 (p1-3-7): 12.7.关于Lebesgue测度的遍历性 43 (p1-4): 第13章 扭转映射 43 (p1-4-1): 13.1.正则性引理 45 (p1-4-2): 13.2.Aubry-Mather集与同宿轨道的存在性 54 (p1-4-3): 13.3.作用量泛函,极小轨道与有序轨道 60 (p1-4-4): 13.4.同宿于Aubry-Mather集的轨道 67 (p1-4-5): 13.5.不变圆周的不存在性与Aubry-Mather集的局部化 71 (p1-5): 第14章 曲面上的流与有关动力系统 72 (p1-5-1): 14.1.Poincaré-Bendixson理论 76 (p1-5-2): 14.2.环面上的无不动点流 79 (p1-5-3): 14.3.极小集 83 (p1-5-4): 14.4.新现象 88 (p1-5-5): 14.5.区间交换变换 96 (p1-5-6): 14.6.在流和弹子球中的应用 99 (p1-5-7): 14.7.旋转数的推广 107 (p1-6): 第15章 区间上的连续映射 107 (p1-6-1): 15.1.Markov覆盖与Markov分割 111 (p1-6-2): 15.2.熵,周期轨道与马蹄 118 (p1-6-3): 15.3.Sharkovsky定理 123 (p1-6-4): 15.4.具有零拓扑熵的映射 128 (p1-6-5): 15.5.折叠理论 131 (p1-6-6): 15.6.帐篷模型 137 (p1-7): 第16章 区间上的光滑映射 137 (p1-7-1): 16.1.双曲排斥极的结构 138 (p1-7-2): 16.2.光滑映射的双曲集 143 (p1-7-3): 16.3.熵的连续性 144 (p1-7-4): 16.4.单峰映射的完全族 149 (p2): 第4部分 双曲动力系统 149 (p2-1): 第17章 例子纵览 150 (p2-1-1): 17.1.Smale吸引子 155 (p2-1-2): 17.2.DA(由 Anosov导出的)映射和Plykin吸引子 159 (p2-1-3): 17.3.诣零流形的扩张映射与Anosov自同构 162 (p2-1-4): 17.4.流的双曲集定义与基本性质 166 (p2-1-5): 17.5.负常数曲率曲面上的测地流 168 (p2-1-6): 17.6.具有负截面曲率的紧Riemann流形上的测地流 172 (p2-1-7): 17.7.秩1对称空间上的测地流 176 (p2-1-8): 17.8.复平面中的双曲Julia集 181 (p2-2): 第18章 双曲集的拓扑性质 181 (p2-2-1): 18.1.伪轨的跟踪 187 (p2-2-2): 18.2.双曲集的稳定性与Markov逼近 190 (p2-2-3): 18.3.谱分解和碎轨 196 (p2-2-4): 18.4.局部积结构 198 (p2-2-5): 18.5.周期轨道的密度与增长 202 (p2-2-6): 18.6. 面上Anosov微分同胚的大范围分类 206 (p2-2-7): 18.7.Markov分割 213 (p2-3): 第19章 双曲集的度量结构 213 (p2-3-1): 19.1.H?lder结构 224 (p2-3-2): 19.2.双曲动力系统中的上同调方程 229 (p2-4): 第20章 平衡态与光滑不变测度 229 (p2-4-1): 20.1.Bowen测度 236 (p2-4-2): 20.2.压力与变分原理 242 (p2-4-3): 20.3.平衡态的唯一性与分类 251 (p2-4-4): 20.4.光滑不变测度 256 (p2-4-5): 20.5.Margulis测度 264 (p2-4-6): 20.6.周期点增长的乘性渐近 273 (p3): 补 遗 273 (p3-1): S 具有非一致双曲性态的动力系统 273 (p3-1-1): S.1.引言 274 (p3-1-2): S.2.Lyapunov指数 286 (p3-1-3): S.3.正则邻域 292 (p3-1-4): S.4.双曲测度 307 (p3-1-5): S.5.双曲测度的熵与动力学 317 (p4): 附 录 317 (p4-1): A 基础知识 317 (p4-1-1): A.1.基本拓扑 325 (p4-1-2): A.2.泛函分析 329 (p4-1-3): A.3.微分流形 341 (p4-1-4): A.4.微分几何 343 (p4-1-5): A.5.曲面的拓扑与几何 345 (p4-1-6): A.6.测度论 349 (p4-1-7): A.7.同调论 352 (p4-1-8): A.8.局部紧群与Lie 355 (p5): 附注 365 (p6): 练习提示与答案 373 (p7): 参考文献 395 (p8): 索引

Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure-preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type.The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis

1 (p1): 0.INTRODUCTION 1 (p1-1): 1.Principal branches of dynamics 6 (p1-2): 2.Flows,vector fields,differential equations 8 (p1-3): 3.Time-one map,section,suspension 10 (p1-4): 4.Linearization and localization 15 (p2): Part 1 Examples and fundamental concepts 15 (p2-1): 1.FIRST EXAMPLES 15 (p2-1-1): 1.Maps with stable asymptotic behavior 19 (p2-1-2): 2.Linear maps 26 (p2-1-3): 3.Rotations of the circle 28 (p2-1-4): 4.Translations on the torus 32 (p2-1-5): 5.Linear flow on the torus and completely integrable systems 35 (p2-1-6): 6.Gradient flows 39 (p2-1-7): 7.Expanding maps 42 (p2-1-8): 8.Hyperbolic toral automorphisms 47 (p2-1-9): 9.Symbolic dynamical systems 57 (p2-2): 2.EQUIVALENCE,CLASSIFICATION,AND INVARIANTS 57 (p2-2-1): 1.Smooth conjugacy and moduli for maps 64 (p2-2-2): 2.Smooth conjugacy and time change for flows 68 (p2-2-3): 3.Topological conjugacy,factors,and structural stability 71 (p2-2-4): 4.Topological classification of expanding maps on a circle 79 (p2-2-5): 5.Coding,horseshoes,and Markov partitions 87 (p2-2-6): 6.Stability of hyperbolic toral automorphisms 90 (p2-2-7): 7.The fast-converging iteration method(Newton method)for the conjugacy problem 94 (p2-2-8): 8.The Poincaré-Siegel Theorem 100 (p2-2-9): 9.Cocycles and cohomological equations 105 (p2-3): 3.PRINCIPAL CLASSES OF ASYMPTOTIC TOPOLOGICAL INVARIANTS 105 (p2-3-1): 1.Growth of orbits 119 (p2-3-2): 2.Examples of calculation of topological entropy 128 (p2-3-3): 3.Recurrence properties 133 (p2-4): 4.STATISTICAL BEHAVIOR OF ORBITS AND INTRODUCTION TO ERGODIC THEORY 133 (p2-4-1): 1.Asymptotic distribution and statistical behavior of orbits 146 (p2-4-2): 2.Examples of ergodicity;mixing 161 (p2-4-3): 3.Measure-theoretic entropy 173 (p2-4-4): 4.Examples of calculation of measure-theoretic entropy 179 (p2-4-5): 5.The Variational Principle 183 (p2-5): 5.SYSTEMS WITH SMOOTH INVARIANT MEASURES AND MORE EXAMPLES 183 (p2-5-1): 1.Existence of smooth invariant measures 196 (p2-5-2): 2.Examples of Newtonian systems 200 (p2-5-3): 3.Lagrangian mechanics 205 (p2-5-4): 4.Examples of geodesic flows 219 (p2-5-5): 5.Hamiltonian systems 229 (p2-5-6): 6.Contact systems 233 (p2-5-7): 7.Algebraic dynamics:Homogeneous and affine systems 237 (p3): Part 2 Local analysis and orbit growth 237 (p3-1): 6.LOCAL HYPERBOLIC THEORY AND ITS APPLICATIONS 237 (p3-1-1): 1.Introduction 239 (p3-1-2): 2.Stable and unstable manifolds 260 (p3-1-3): 3.Local stability of a hyperbolic periodic point 263 (p3-1-4): 4.Hyperbolic sets 273 (p3-1-5): 5.Homoclinic points and horseshoes 278 (p3-1-6): 6.Local smooth linearization and normal forms 287 (p3-2): 7.TRANSVERSALITY AND GENERICITY 287 (p3-2-1): 1.Generic properties of dynamical systems 290 (p3-2-2): 2.Genericity of systems with hyperbolic periodic points 298 (p3-2-3): 3.Nontransversality and bifurcations 304 (p3-2-4): 4.The theorem of Artin and Mazur 307 (p3-3): 8.ORBIT GROWTH ARISING FROM TOPOLOGY 308 (p3-3-1): 1.Topological and fundamental-group entropies 310 (p3-3-2): 2.A survey of degree theory 316 (p3-3-3): 3.Degree and topological entropy 318 (p3-3-4): 4.Index theory for an isolated fixed point 323 (p3-3-5): 5.The role of smoothness:The Shub-Sullivan Theorem 326 (p3-3-6): 6.The Lefschetz Fixed-Point Formula and applications 330 (p3-3-7): 7.Nielsen theory and periodic points for toral maps 335 (p3-4): 9.VARIATIONAL ASPECTS OF DYNAMICS 336 (p3-4-1): 1.Critical points of functions,Morse theory,and dynamics 339 (p3-4-2): 2.The billiard problem 349 (p3-4-3): 3.Twist maps 365 (p3-4-4): 4.Variational description of Lagrangian systems 367 (p3-4-5): 5.Local theory and the exponential map 372 (p3-4-6): 6.Minimal geodesics 376 (p3-4-7): 7.Minimal geodesics on compact surfaces 381 (p4): Part 3 Low-dimensional phenomena 381 (p4-1): 10.INTRODUCTION:WHAT IS LOW-DIMENSIONAL DYNAMICS? 387 (p4-2): 11.HOMEOMORPHISMS OF THE CIRCLE 387 (p4-2-1): 1.Rotation number 393 (p4-2-2): 2.The Poincaré classification 401 (p4-3): 12.CIRCLE DIFFEOMORPHISMS 401 (p4-3-1): 1.The Denjoy Theorem 403 (p4-3-2): 2.The Denjoy example 405 (p4-3-3): 3.Local analytic conjugacies for Diophantine rotation number 410 (p4-3-4): 4.Invariant measures and regularity of conjugacies 412 (p4-3-5): 5.An example with singular conjugacy 415 (p4-3-6): 6.Fast-approximation methods 419 (p4-3-7): 7.Ergodicity with respect to Lebesgue measure 423 (p4-4): 13.TWIST MAPS 424 (p4-4-1): 1.The Regularity Lemma 425 (p4-4-2): 2.Existence of Aubry-Mather sets and homoclinic orbits 434 (p4-4-3): 3.Action functionals,minimal and ordered orbits 441 (p4-4-4): 4.Orbits homoclinic to Aubry-Mather sets 447 (p4-4-5): 5.Nonexistence of invariant circles and localization of Aubry-Mather sets 451 (p4-5): 14.FLOWS ON SURFACES AND RELATED DYNAMICAL SYSTEMS 452 (p4-5-1): 1.Poincaré-Bendixson theory 457 (p4-5-2): 2.Fixed-point-free flows on the torus 460 (p4-5-3): 3.Minimal sets 464 (p4-5-4): 4.New phenomena 470 (p4-5-5): 5.Interval exchange transformations 479 (p4-5-6): 6.Application to flows and billiards 483 (p4-5-7): 7.Generalizations of rotation number 489 (p4-6): 15.CONTINUOUS MAPS OF THE INTERVAL 489 (p4-6-1): 1.Markov covers and partitions 493 (p4-6-2): 2.Entropy,periodic orbits,and horseshoes 500 (p4-6-3): 3.The Sharkovsky Theorem 505 (p4-6-4): 4.Maps with zero topological entropy 511 (p4-6-5): 5.The kneading theory 514 (p4-6-6): 6.The tent model 519 (p4-7): 16.SMOOTH MAPS OF THE INTERVAL 519 (p4-7-1): 1.The structure of hyperbolic repellers 520 (p4-7-2): 2.Hyperbolic sets for smooth maps 525 (p4-7-3): 3.Continuity of entropy 526 (p4-7-4): 4.Full families of unimodal maps 531 (p5): Part 4 Hyperbolic dynamical systems 531 (p5-1): 17.SURVEY OF EXAMPLES 532 (p5-1-1): 1.The Smale attractor 537 (p5-1-2): 2.The DA(derived from Anosov)map and the Plykin attractor 541 (p5-1-3): 3.Expanding maps and Anosov automorphisms of nilmanifolds 544 (p5-1-4): 4.Definitions and basic properties of hyperbolic sets for flows 549 (p5-1-5): 5.Geodesic flows on surfaces of constant negative curvature 551 (p5-1-6): 6.Geodesic flows on compact Riemannian manifolds with negative sectional curvature 555 (p5-1-7): 7.Geodesic flows on rank-one symmetric spaces 559 (p5-1-8): 8.Hyperbolic Julia sets in the complex plane 565 (p5-2): 18.TOPOLOGICAL PROPERTIES OF HYPERBOLIC SETS 565 (p5-2-1): 1.Shadowing of pseudo-orbits 571 (p5-2-2): 2.Stability of hyperbolic sets and Markov approximation 574 (p5-2-3): 3.Spectral decomposition and specification 581 (p5-2-4): 4.Local product structure 583 (p5-2-5): 5.Density and growth of periodic orbits 587 (p5-2-6): 6.Global classification of Anosov diffeomorphisms on tori 591 (p5-2-7): 7.Markov partitions 597 (p5-3): 19.METRIC STRUCTURE OF HYPERBOLIC SETS 597 (p5-3-1): 1.H?lder structures 608 (p5-3-2): 2.Cohomological equations over hyperbolic dynamical systems 615 (p5-4): 20.EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES 615 (p5-4-1): 1.Bowen measure 623 (p5-4-2): 2.Pressure and the variational principle 628 (p5-4-3): 3.Uniqueness and classification of equilibrium states 637 (p5-4-4): 4.Smooth invariant measures 643 (p5-4-5): 5.Margulis measure 651 (p5-4-6): 6.Multiplicative asymptotic for growth of periodic points 659 (p6): Supplement 659 (p6-1): S.DYNAMICAL SYSTEMS WITH NONUNIFORMLY HYPERBOLIC BEHAVIOR BY ANATOLE KATOK AND LEONARDO MENDOZA 659 (p6-1-1): 1.Introduction 660 (p6-1-2): 2.Lyapunov exponents 672 (p6-1-3): 3.Regular neighborhoods 678 (p6-1-4): 4.Hyperbolic measures 693 (p6-1-5): 5.Entropy and dynamics of hyperbolic measures 703 (p6-1-6): Appendix 703 (p6-2): A.BACKGROUND MATERIAL 703 (p6-2-1): 1.Basic topology 711 (p6-2-2): 2.Functional analysis 715 (p6-2-3): 3.Differentiable manifolds 727 (p6-2-4): 4.Differential geometry 730 (p6-2-5): 5.Topology and geometry of surfaces 731 (p6-2-6): 6.Measure theory 735 (p6-2-7): 7.Homology theory 738 (p6-2-8): 8.Locally compact groups and Lie groups 741 (p7): NOTES 765 (p8): HINTS AND ANSWERS TO THE EXERCISES 781 (p9): REFERENCES 793 (p10): INDEX

"This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems"-- "In a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"--

"This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems"-- "In a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"--

Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure-preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type.The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis

<p>Presenting a wide cross-section of current research in the theory of dynamical systems, this collection consists of articles by leading researchers (and several Fields medallists) in a variety of specialties. Surveys featuring new results, as well as research papers, are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, and applications. The target audience is dynamicists, as well as mathematicians from other disciplines.</p>

Каток вибрационный DYNAPAC CC 422/422C/CC 422HF/CC 422CHF/CC 432 CC 522/522C/CC 522HF/522CHF Руководство по эксплуатации В данном Руководстве содержатся сведения по эксплуатации катка. Информация по техническому обслуживанию приведена в "РУКОВОДСТВЕ ПО ТЕХНИЧЕСКОМУ ОБСЛУЖИВАНИЮ катков СС 422/422С/СС 422HF/CC 422CHF/CC 432 СС 522/522С/СС 522HF/522CHF". Dynapac CC 422 - вибрационный каток, класса 10-тонных машин, с шарнирно-сочлененной рамой, с приводом, тормозом, и вибрацией обоих вальцов. Этот каток выпускается также в так называемом исполнении Комби, и имеет обозначение CC 422C. Он весит около 9 тонн и имеет вибрационный валец спереди и четыре гладких резиновых шины сзади, с передним и задним приводом и тормозом. СС432 - вибрационный каток класса 11-тоных машин, с шарнирно-сочлененной рамой и вибрацией обоих вальцов. СС522 - так обозначается самый крупный каток в этой серии. Он относится к классу 12-тонных машин, и, по сравнению с катком СС422, его вальцы более широкие и имеют больший диаметр. Этот каток также выпускается в исполнении Комби, имеет обозначение СС522С, и весит 11 тонн.