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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 lev

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 lev

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.

本書對動力系統理論提供了一個全面廣泛的綜合介紹，是現代動力系統理論的一本難得的並將在今後相當長時間內有著一定影響的經典著作。它內容博大精深，是涵蓋當代動力系統幾乎各個分支基本理論的一部鴻篇巨制。作者介紹並發展了這些理論，同時也給應用中對此理論感興趣的研究人員提供了基本工具和範例。

本書包含兩部分內容：第一部分是入門教程，主要介紹動力系統基本知識，作者通過對壓縮映射、線性系統、簡單二次映射、低維保守系統、彈子球、圓周和環面系統的介紹，引入了回復性、等度分布、拓撲傳遞、混沌、拓撲熵、編碼等一系列描述動力系統漸近行為的概念和工具；第二部分是發展概述，主要介紹動力系統研究的最新進展和應用，討論了一致和非一致雙曲系統、同宿結、奇異吸引子、扭轉映射、閉測地線，以及動力系統在數論中的應用