本书共分十章，主要介绍了有限维空间混沌映射的基本理论，其内容包括一维动力系统（区间映射）、分岔、一般拓扑、符号动力系统、分形和一类由区间映射导出的无限维动力系统，以及混沌映射的快速涨落，这是作者近年来提出的新观点。为了便于读者从离散时间动力系统过渡到由常微分方程和偏微分方程控制的连续时间动力系统，本书还给出了两个附录。本书由动力学系统和混沌理论研究生入门课程的课堂讲稿编写而成，适合高等院校研究生及相关专业的爱好者参考阅读。

陈功，was born in Kaohsiung, Taiwan in 1950. He received his BSc (Math) from the National Tsing Hua University in Hsinchu, Taiwan in 1972 and PhD (Math) from the University of Wisconsin at Madison in 1977. He has taught at the Southern Illinois University at Carbondale (1977-78), and the Pennsylvania State University at University Park (1978-1987). Since 1987, he has been Professor of Mathematics and Aerospace Engineering, and (since 2000) a member of the Institute for Quantum Science and Engineering, at Texas A&M University in College Station, Texas. Since 2010, he is also Professor of Mathematics at Texas A&M University in Qatar at Doha, Qatar.

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
编辑手记