Acta Mathematica Vietnamica

2013, Volume 38, Issue 1, pp 11-19


A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy
James Montaldi, Miguel Rodríguez-Olmos

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.

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