Series Preface Preface to the Second Edition Introduction 1 Equilibrium Solutions，Stability,and Linearized Stability 1.1 Equilibria of Vector Fields 1.2 Stability of Trajectories 1.2a Linearization 1.3 Maps 1.3a Definitions of Stability for Maps 1.3b Stability of Fixed Points of Linear Maps 1.3c Stability of Fixed Points of Maps via the Linear Approximation 1.4 Some Terminology Associated with Fixed Points 1.5 Application to the Unforced Duffing Oscillator 1.6 Exercises 2 Liapunov Functions 3 Invariant Manifolds：Linear and Nonlinear Systems 4 Periodic Orbits 5 Vector Fields Possessing an Integral 6 Index Theory 7 Some General Properties of Vector Fields: Existence，Uniqueness，Differentiability,and Flows 8 Asymptotic Behavior 9 The Poinear6-Bendixson Theorem 10 Poinear6 Maps 11 Conjugacies of Maps，and Varying the Cross.Section 12 Structural Stability，Genericity，and Transversality 13 Lagrange's Equations 14 Hamiltonian vector Fields 15 Gradient vector Fields 16 Reversible Dynamical Systems 17 Asymptotically Autonomous Vector Fields 18 Center Manifolds 19 Normal Forms 20 Bifurcation of Fixed Points of Vector Fields 21 Bifurcations of Fixed Points of Maps 23 The Smale Horseshoe 24 Symbolic Dynamics 25 The Conley-Moser Conditions，or「How to Prove That a Dynamical System is Chaotic」 26 Dynamics Near Homoclinic Points ofTwo-Dimensional Maps 27 Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous V.ector Fields 28 Melnikov's Method for Homoclinic Orbits in Two-Dimensional，Time-Periodic Vector Fields 29 Liapunov Exponents 30 Chaos and Strange Attractors 31 Hyperbolic Invariant Sets：A Chaotic Saddle 32 Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems 33 Global Bifurcations Arising from Local Codimension--Two Bifurcations 34 Glossary of Frequently Used Terms Bibliography Index
[