A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy

Montaldi, James and Rodriguez-Olmos, Miguel (2013) A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy. Acta Mathematica Vietnamica, 38 (1). pp. 11-19. ISSN 0251-4184

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Abstract

We present a framework for the study of the local qualitative dynamics of equivariant Hamiltonian flows specially designed for points in phase space with nontrivial 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.

Item Type: Article
Uncontrolled Keywords: Hamiltonian systems, momentum map, bifurcations, continuous isotropy
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User: Dr James Montaldi
Date Deposited: 21 Nov 2012
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1915

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