Geometric Theory of Dynamical Systems An Introduction [Paperback]

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 Poincar? 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.Springer Book Archives