●Preface
1 Simple Interval Maps and Their Iterations
1.1 Introduction
1.2 The Inverse and hnplicit Function Theorems
1.3 Visualizing from the Graphics oflterations of the Quadratic Map
Notes for Chapter 1
2 Total Variations of Iterates of Maps
2.1 The Use of Total Variations as a Measure of Chaos
Notes for Chapter 2
3 Ordering among Periods: The Sharkovski Theorem
Notes for Chapter 3
4 Bifurcation Theorems for Maps
4.1 The Period-Doubling Bifurcation Theorem
4.2 Saddle-Node Bifurcations
4.3 The Pitchfork Bifurcation
4.4 Hopf Bifurcation
Notes for Chapter 4
5 Homoclinicity. LyapunoffExponents
5.1 Homoclinic Orbits
5.2 Lyapunoff Exponents
Notes for Chapter 5
6 Symbolic Dynamics, Conjugacy and Shift Invariant Sets
6.1 The Itinerary of an Orbit
6.2 Properties of the shift map σ
6.3 Symbolic Dynamical Systems Σk and Σk+
6.4 The Dynamics of (Σl+，σ+) and Chaos
6.5 Topological Conjugacy and Semiconjugacy
6.6 Shift Im, ariant Sets
6.7 Construction of Shift Invariant Sets
6.8 Snap-back Repeller as a Shift Invariant Set
Notes for Chapter 6
7 The Smale Horseshoe
7.1 The Standard Smale Horseshoe
7.2 The General Horseshoe
Notes for Chapter 7
8 Fractals
8.1 Examples of Fractals
8.2 HausdorffDimension and the HausdorffMeasure
8.3 Iterated Function Systems (IFS)
Notes fbr Chapter 8
9 Rapid Fluctuations of Chaotic Maps on RN
9.1 Total Variation for Vector-Value Maps
9.2 Rapid Fluctuations of Maps on ]RN
9.3 Rapid Fluctuations of Systems with Quasi-shift Invariant Sets
9.4 Rapid Fluctuations of Systems Containing Topological Horseshoes
9.5 Examples of Applications of Rapid Fluctuatkms
Notes for Chapter 9
10 Infinite-dimensional Systems Induced by Continuous-Time Difference Equations
10.1 I3DS
10.2 Rates of Growth of Total Varkations of Iterates
10.3 Properties of the Set B(f)
10.4 Properties of the Set U(f)
10.5 Properties of the Set E(f)
Notes for Chapter 10
A Introduction to Continuous-Time Dynamical Systems
A.1 The Local Behavior of 2-Dimensional Nonlinear Systems
A.2 Index for Two-Dimensional Systems
A.3 The Poincard Map for a Periodic Orbit in RN
B Chaotic Vibration of the Wave Equation due to Energy Pumping and van der Pol Boundary Conditions
B.1 The Mathematical Model and Motivations
B.2 Chaotic Vibration of the Wave Equation
Bibliography
Authors' Biographies
Index
編輯手記

本書共分十章，主要介紹了有限維空間混沌映射的基本理論，其內容包括一維動力繫統（區間映射）、分岔、一般拓撲、符號動力繫統、分形和一類由區間映射導出的無限維動力繫統，以及混沌映射的快速漲落，這是作者近年來提出的新觀點。為了便於讀者從離散時間動力繫統過渡到由常微分方程和偏微分方程控制的連續時間動力繫統，本書還給出了兩個附錄。
本書由動力學繫統和混沌理論研究生入門課程的課堂講稿編寫而成，適合高等院校研究生及相關專業的愛好者參考閱讀。