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2005.39: Openness of momentum maps and persistence of extremal relative equilibria

2005.39: James Montaldi and Tadashi Tokieda (2003) Openness of momentum maps and persistence of extremal relative equilibria. Topology, 42. pp. 833-844. ISSN 0040-9383

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DOI: 10.1016/S0040-9383(02)00047-2

Abstract

We prove that for every proper Hamiltonian action of a Lie group G in finite dimensions the momentum map is locally G-open relative to its image (i.e. images of G-invariant open sets are open). As an application we deduce that in a Hamiltonian system with continuous Hamiltonian symmetries, extremal relative equilibria persist for every perturbation of the value of the momentum map, provided the isotropy subgroup of this value is compact. We also demonstrate how this persistence result applies to an example of ellipsoidal figures of rotating fluid. We also provide an example with plane point vortices which shows how the compactness assumption is related to persistence.

Item Type:Article
Uncontrolled Keywords:Hamiltonian systems with symmetry, momentum map, reduction
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 53 Differential geometry
MIMS number:2005.39
Deposited By:Dr James Montaldi
Deposited On:12 December 2005

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