Elements of Differentiable Dynamics and Bifurcation Theory - 1st Edition - ISBN: 9780126017106, 9781483272184

Elements of Differentiable Dynamics and Bifurcation Theory

1st Edition

Authors: David Ruelle
eBook ISBN: 9781483272184
Imprint: Academic Press
Published Date: 28th February 1989
Page Count: 196
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Description

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.

Table of Contents


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

Problem

Part 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

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

Details

No. of pages:
196
Language:
English
Copyright:
© Academic Press 1989
Published:
Imprint:
Academic Press
eBook ISBN:
9781483272184

About the Author

David Ruelle