We present a framework for the study of the local qualitative dynamics of equivariant Hamiltonian flows specially designed for points in phase space with non-trivial isotropy. This is based on the classical construction of structure-preserving tubular neighborhoods for Hamiltonian Lie group actions on symplectic manifolds. This framework is applied to obtaining concrete and testable conditions guaranteeing the existence of bifurcations from symmetric branches of Hamiltonian relative equilibria.
Grup de recerca
DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions