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
