非线性振动、动力学系统和矢量场的分叉 英文影印版 作者： [美] J.古肯海默，P.霍姆斯 著 出版时间：2017年版 内容简介 本书是论述动力学系统、分叉理论与非线性振动研究之间接口部分的理论专著，主要讨论以欧氏空间微分流形为相空间，以及常微分方程组和映象集为数学模型的问题。本书初版于1983年，本版是2002第7次修订版，该书出版三十余年来倍受读者欢迎，是混沌动力学的经典教材。 目录 CHAPTER 1 Introduction： Differential Equations and Dynamical Systems 1.1 Existence and Uniqueness of Solutions 1.1 The Linear System x = Ax 1.2 Flows and Invariant Subspaces 1.3 The Nonlinear System x = f （x） 1.4 Linear and Nonlinear Maps 1.5 Closed Orbits， Poincare Maps.and Forced Oscillations 1.6 Asymptotic Behavior 1.7 Equivalence Relations and Structural Stability 1.8 Two-Dimensional Flows 1.9 Peixoto's Theorem for Two-Dimensional Flows
CHAPTER 2 An Introduction to Chaos： Four Examples 2.1 Van der Pol's Equation 2.2 Duffing's Equaiion 2.3 The Lorenz Equations 2.4 The Dynamics of a Bouncing Ball 2.5 Conclusions： The Moral of the Tales
CHAPTER 3 Local Bifurcations 3.1 BiFurcation Problems 3.2 Center Manifolds 3.3 Normal Forms 3.4 Codimension One Bifurcations of Equilibria 3.5 Codimension One Bifurcations of Maps and Periodic Orbits
CHAPTER 4 Averaging and Perturbation from a Geometric Viewpoint 4.1 Averaging and Poincare Maps 4.2 Examples of Averaging 4.3 Averaging and Local Bifurcations 4.4 Averaging， Hamikonian Systems， and Global Behavior： Cautionary Notes 4.5 Melnikov's Method： Perturbations of Planar Homoclinic Orbits 4.6 Melnikov's Method： Perturbations of Hamiltonian Systems and Subharmonic Orbits 4.7 Stability or Subharmonic Orbits 4.8 Two Degree of Freedom Hamiltonians and Area Preserving Maps of the Plane
CHAPTER 5 Hyperbolic Sets， Symbolic Dynamics， and Strange Attractors 5.0 Introduction 5.1 The Smale Horseshoe： An Example of a Hyperbolic Limit Set 5.2 Invariant Sets and Hyperbolicity 5.3 Markov Partitions and Symbolic Dynamics 5.4 Strange Auractors and the Stability Dogma 5.5 Structurally Stable Attractors 5.6 One-Dimensional Evidence for Strange Attractors 5.7 The Geometric Lorenz Attractor 5.8 Statistical Properties： Dimension， Entropy， and Liapunov Exponents
CHAPTER 6 Global Bifurcations 6.1 Saddle Connections 6.2 Rotation Numbers 6.3 Bifurcations or One-Dimensional Maps 6.4 The Lorenz Bifurcations 6.5 Homoclinic Orbits in Three-Dimensional Flows： Silnikov's Example 6.6 Homoclinic aifurcations of Periodic Orbits 6.7 Wild Hyperbolic Sets 68 Renormalization and Universality
CHAPTER 7 Local Codimension Two Bifurcations of Flows 7.1 Degeneracy in Higher-Order Terms 7.2 A Note on k-Jets and Determinacy 7.3 The Double Zero Eigenvalue 7.4 A Pure Imaginary Pair and a Simple Zero Eigenvalue 7.5 Two Pure Imaginary Pairs of Eigenvalues without Resonance 7.6 Applicaiions to Large Systems APPENDIX Suggestions for Further Reading Postscript Added at Second Printing Glossary References Index
