ABSTRACT

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.

chapter Chapter 1|10 pages

Introduction & preliminaries

chapter Chapter 2|14 pages

Hyperoctahedral groups

chapter Chapter 3|7 pages

A zoo of bifurcations

chapter Chapter 4|18 pages

Stability and determinacy

chapter Chapter 5|8 pages

The invariant sphere theorem

chapter Chapter 6|23 pages

Heteroclinic cycles in equivariant bifurcations

chapter Chapter 7|20 pages

Symmetrically coupled cell systems

chapter Chapter 9|17 pages

Geometric methods