Geometric Theory of Dynamical Systems

Inhaltsverzeichnis

• 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 Poincaré 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.
• References.