Elements of Differentiable Dynamics and Bifurcation Theory
- 1st Edition - February 28, 1989
- Latest edition
- Author: David Ruelle
- Language: English
Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is… Read more
Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.
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
- Edition: 1
- Latest edition
- Published: February 28, 1989
- Language: English
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