连续和离散动力系统引论（第二版 影印版）

　　本书从数学的角度初步介绍了定性微分方程和离散动力系统，包括了理论性证明、计算方法和应用。全书分两部分，即微分方程的连续时间和动力系统的离散时间，可分别用于一学期的课程， 或两者结合为一年期的课程。微分方程的素材通过任意维数的线性系统介绍了定性的或几何的方法。接下来的几章中平衡性是*重要的特点，其中标量（能量） 函数为主要工具，在那里出现了周期轨道，*后还讨论了微分方程的混沌系统。通过例题和定理引进了许多不同的方法。离散动力系统的素材是从单变量的映射着手的，然后继续进到高维体系中。处理论题则从具有明显的周期点的例子开始， 然后对那些可证明它们存在但不能给出显式形式的分析引进了符号动力学。混沌系统既可数学地表示也可用更具计算性的Lyapunov 指数表示。以一维映射为模型，多重映射则被用来讲述高维的同一素材。这个高维素材不那么具有可计算性，而是更具概念性和理论性。关于分形的*后一章引进了各种维数，它是度量一个系统复杂性的另一个计算工具。它也处理了迭代函数系统，其给出了复杂集合的例子。在此书的第二版中，许多素材已被重写以使表述更清楚。另外，书的两部分都添进了一些新的材料。此书可以用作大学高年级的常微分方程和/或动力系统课程的教科书。预备知识是微积分的标准课程（单变量和多变量的）、线性代数和微分方程初阶。

暂缺《连续和离散动力系统引论（第二版 影印版）》作者简介

Preface Historical Prologue Part 1. Systems of Nonlinear Differential Equations Chapter 1. Geometric Approach to Differential Equations Chapter 2. Linear Systems 2.1. Fundamental Set of Solutions Exercises 2.1 2.2. Constant Coefficients： Solutions and Phase Portraits Exercises 2.2 2.3. Nonhomogeneous Systems： Time-dependent Forcing Exercises 2.3 2.4. Applications Exercises 2.4 2.5. Theory and Proofs Chapter 3. The Flow： Solutions of Nonlinear Equations 3.1. Solutions of Nonlinear Equations Exercises 3.1 3.2. Numerical Solutions of Differential Equations Exercises 3.2 3.3. Theory and Proofs Chapter 4. Phase Portraits with Emphasis on Fixed Points 4.1. Limit Sets Exercises 4.1 4.2. Stability of Fixed Points Exercises 4.2 4.3. Scalar Equations Exercises 4.3 4.4. Two Dimensions and Nullclines Exercises 4.4 4.5. Linearized Stability of Fixed Points Exercises 4.5 4.6. Competitive Populations Exercises 4.6 4.7. Applications Exercises 4.7 4.8. Theory and Proofs Chapter 5. Phase Portraits Using Scalar Functions 5.1. Predator-Prey Systems Exercises 5.1 5.2. Undamped Forces Exercises 5.2 5.3. Lyapunov Functions for Damped Systems Exercises 5.3 5.4. Bounding Functions Exercises 5.4 5.5. Gradient Systems Exercises 5.5 5.6. Applications Exercises 5.6 5.7. Theory and Proofs Chapter 6. Periodic Orbits 6.1. Introduction to Periodic Orbits Exercises 6.1 6.2. Poincare-Bendixson Theorem Exercises 6.2 6.3. Self-Excited Oscillator Exercises 6.3 6.4. Andronov-HopfBifurcation Exercises 6.4 6.5. Homoclinic Bifurcation Exercises 6.5 6.6. Rate of Change of Volume Exercises 6.6 6.7. Poincare Map Exercises 6.7 6.8. Applications Exercises 6.8 6.9. Theory and Proofs Chapter 7. Chaotic Attractors 7.1. Attractors Exercises 7.1 7.2. Chaotic Attractors Exercise 7.2 7.3. Lorenz System Exercises 7.3 7.4. RSssler Attractor Exercises 7.4 7.5. Forced Oscillator Exercises 7.5 7.6. Lyapunov Exponents Exercises 7.6 7.7. Test for Chaotic Attractors Exercises 7.7 7.8. Applications 7.9. Theory and Proofs Part 2. Iteration of Functions Chapter 8. Iteration of Functions as Dynamics 8.1. One-Dimensional Maps 8.2. Functions with Several Variables Chapter 9. Periodic Points of One-Dimensional Maps 9.1. Periodic Points Exercises 9.1 9.2. Iteration Using the Graph Exercises 9.2 9.3. Stability of Periodic Points Exercises 9.3 9.4. Critical Points and Basins Exercises 9.4 9.5. Bifurcation of Periodic Points Exercises 9.5 9.6. Conjugacy Exercises 9.6 9.7. Applications Exercises 9.7 9.8. Theory and Proofs Chapter 10. Itineraries for One-Dimensional Maps 10.1. Periodic Points from Transition Graphs Exercises 10.1 10.2. Topological Transitivity Exercises 10.2 10.3. Sequences of Symbols Exercises 10.3 10.4. Sensitive Dependence on Initial Conditions Exercises 10.4 10.5. Cantor Sets Exercises 10.5 10.6. Piecewise Expanding Maps and Subshifts Exercises 10.6 10.7. Applications Exercises 10.7 10.8. Theory and Proofs Chapter 11. Invariant Sets for One-Dimensional Maps 11.1. Limit Sets Exercises 11.1 11.2. Chaotic Attractors Exercises 11.2 11.3. Lyapunov Exponents Exercises 11.3 11.4. Invariant Measures Exercises 11.4 11.5. Applications 11.6. Theory and Proofs Chapter 12. Periodic Points of Higher Dimensional Maps 12.1. Dynamics of Linear Maps Exercises 12.1 12.2. Classification of Periodic Points Exercises 12.2 12.3. Stable Manifolds Exercises 12.3 12.4. Hyperbolic Toral Automorphisms Exercises 12.4 12.5. Applications Exercises 12.5 12.6. Theory and Proofs Chapter 13. Invariant Sets for Higher Dimensional Maps 13.1. Geometric Horseshoe Exercises 13.1 13.2. Symbolic Dynamics Exercises 13.2 13.3. Homoclinic Points and Horseshoes Exercises 13.3 13.4. Attractors Exercises 13.4 13.5. Lyapunov Exponents Exercises 13.5 13.6. Applications 13.7. Theory and Proofs Chapter 14. Fractals 14.1. Box Dimension Exercises 14.1 14.2. Dimension of Orbits Exercises 14.2 14.3. Iterated-Function Systems Exercises 14.3 14.4. Theory and Proofs Appendix A. Background and Terminology A.1. Calculus Background and Notation A.2. Analysis and Topology Terminology A.3. Matrix Algebra Appendix B. Generic Properties Bibliography Index