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Geometric Theory of Dynamical Systems
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Table of Contents

1 Differentiable Manifolds and Vector Fields.- 0 Calculus in ?n and Differentiable Manifolds.- 1 Vector Fields on Manifolds.- 2 The Topology of the Space of Cr Maps.- 3 Transversality.- 4 Structural Stability.- 2 Local Stability.- 1 The Tubular Flow Theorem.- 2 Linear Vector Fields.- 3 Singularities and Hyperbolic Fixed Points.- 4 Local Stability.- 5 Local Classification.- 6 Invariant Manifolds.- 7 The ?-lemma (Inclination Lemma). Geometrical Proof of Local Stability.- 3 The Kupka-Smale Theorem.- 1 The Poincare Map.- 2 Genericity of Vector Fields Whose Closed Orbits Are Hyperbolic.- 3 Transversality of the Invariant Manifolds.- 4 Genericity and Stability of Morse-Smale Vector Fields.- 1 Morse-Smale Vector Fields; Structural Stability.- 2 Density of Morse-Smale Vector Fields on Orientable Surfaces.- 3 Generalizations.- 4 General Comments on Structural Stability. Other Topics.- Appendix: Rotation Number and Cherry Flows.- References.

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