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2012.111: A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy

2012.111: James Montaldi and Miguel Rodriguez-Olmos (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 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 70 Mechanics of particles and systems
MIMS number:2012.111
Deposited By:Dr James Montaldi
Deposited On:21 November 2012

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