Lectures on Bifurcations, Dynamics and Symmetry

✍ Scribed by Michael J. Field (Author)

• Publisher: Chapman and Hall/CRC
• Year: 1996
• Leaves: 168
• Edition: 1
• Category: Library

✦ Synopsis

This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. This text covers a wide range of current results in the subject of bifurcations, dynamics and symmetry. The style and format of the original lectures has largely been maintained and the notes include over 70 exercises.

✦ Table of Contents

Chapter 1. Introduction & preliminaries, Chapter 2. Hyperoctahedral groups, Chapter 3. A zoo of bifurcations, Chapter 4. Stability and determinacy, Chapter 5. The invariant sphere theorem, Chapter 6. Heteroclinic cycles in equivariant bifurcations, Chapter 7. Symmetrically coupled cell systems, Chapter 8. An example of Z2-transversality in a system of four coupled oscillators, Chapter 9. Geometric methods, Appendix A. Converse to the MISC, Hints and solutions to selected exercises, Bibliography, Index