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Elements of Differentiable Dynamics and Bifurcation Theory

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Author(s): David Ruelle
Publisher: Academic Press
Year: 1989

Language: English

Title page
Preface
Part 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
Problems
Part 2. Bifurcations
9. Bifurcations of Fixed Points of a Map
10. Bifurcation of Periodic Orbits. The Case of Semiflows
Il. 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
Problems
Part 3. Appendices
A. Sets, Topology, Metric, Banach Spaces
B. Manifolds
c. Topological Dynamics and Ergodic Theory
D. Axiom A Dynamical Systems
References
Index