Contents -- Foreword -- Preface -- Introduction -- I. The simple pendulum -- II. A dissipative system -- III. The spherical pendulum -- IV. Vector fields and dynamical systems -- Chapter 1. Some Simple Examples -- I. Flows and homeomorphisms -- II. Orbits -- III. Examples of dynamical systems -- IV. Constructing systems -- V. Properties of orbits -- Appendix 1 -- I. Group actions -- Chapter 2. Equivalent Systems -- I. Topological conjugacy -- II. Homeomorphisms of the circle -- III. Flow equivalence and topological equivalence -- IV. Local equivalence -- V. Limit sets of flows -- VI. Limit sets of homeomorphisms -- VII. Non-wandering sets -- Appendix 2 -- I. Two topological lemmas -- II. Oriented orbits in Hausdorff spaces -- III. Compactification -- Chapter 3. Integration of Vector Fields -- I. Vector fields -- II. Velocity vector fields and integral flows -- III. Ordinary differential equations -- IV. Local integrals -- V. Global integrals -- Appendix 3 -- I. Integrals of perturbed vector fields -- II. First integrals -- Chapter 4. Linear Systems -- I. Linear flows on R" -- II. Linear automorphisms of R" -- III. The spectrum of a linear endomorphism -- IV. Hyperbolic linear automorphisms -- V. Hyperbolic linear vector fields -- Appendix 4 -- I. Spectral Theory -- Chapter 5. Linearization -- I. Regular points -- II. Hartman's theorem -- III. Hartman's theorem for flows -- IV. Hyperbolic closed orbits -- Appendix 5 -- I. Smooth linearization -- II. Liapunov stability -- III. The index of a fixed point -- Chapter 6. Stable Manifolds -- I. The stable manifold at a hyperbolic fixed point of a diffeomorphism -- II. Stable manifold theory for flows -- HI. The generalized stable manifold theorem -- Appendix 6 -- I. Perturbed stable manifolds -- Chapter 7. Stable Systems -- I. Low dimensional systems -- II. Anosov systems.

III. Characterization of structural stability -- IV. Density -- V. Omega stability -- VI. Bifurcation -- Appendix A. Theory of Manifolds -- I. Topological manifolds -- II. Smooth manifolds and maps -- III. Smooth vector bundles -- IV. The tangent bundle -- V. Immersions embeddings and submersions -- VI. Sections of vector bundles -- VII. Tensor bundles -- VIII. Riemannian manifolds -- Appendix B. Map Spaces -- I. Spaces of smooth maps -- II. Composition theorems -- III. Spaces of sections -- IV. Spaces of dynamical systems -- Appendix C. The Contraction Mapping Theorem -- Bibliography -- Subject Index.