Elements of Differentiable Dynamics and Bifurcation Theory

PrefacePart 1. Differentiable Dynamical Systems 1. Manifolds 2. Differentiable Dynamics 3. Vector Fields 4. Fixed Points and Periodic Orbits. Poincaré Map 5. Hyperbolic Fixed Points and Periodic Orbits 6. Stable and Unstable Manifolds 7. Center Manifolds 8. Attractors, Bifurcations, Genericity Note ProblemPart 2. Bifurcations 9. Bifurcations of Fixed Points of a Map 10. Bifurcation of Periodic Orbits. The Case of Semiflows 11. The Saddle-Node Bifurcation 12. The Flip Bifurcation 13. The Hopf Bifurcation 14. Persistence of Normally Hyperbolic Manifolds 15. Hyperbolic Sets 16. Homoclinic and Heteroclinic Intersections 17. Global Bifurcations Note ProblemsPart 3. Appendices A. Sets, Topology, Metric, Banach Spaces B. Manifolds C. Topological Dynamics and Ergodic Theory D. Axiom A Dynamical SystemsReferencesIndex