Speaker: Reiner Lauterbach (University of Hamburg)
Title: Absolutely irreducible group actions, the equivariant branching lemma and Hamiltonian systems
Abstract:
We discuss certain symmetry breaking bifurcations on finite dimensional spaces. We review a (slightly generalized) version of the equivariant branching lemma which provides steady state solutions if there is an odd dimensional fixed point subspace. We present examples of group actions which do not have odd dimensional fixed point subspaces.Then it is not clear what kind of bifurcations do occur. We provide examples of interesting bifurcation scenarios for two infinite series of (finite) groups. These groups came up in an attempt to construct examples where there is no steady state bifurcation. Among other things they give rise to equivariant Hamiltonian systems.
Although we cannot answer the fundamental question whether absolutely irreducible group actions necessarily lead to steady state bifurcations, we provide some evidence that generically this should be the case.
Based on a large collection of data we will present some open questions.