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2005.37: Persistence and stability of relative equilibria

2005.37: James Montaldi (1997) Persistence and stability of relative equilibria. Nonlinearity, 10. pp. 449-466. ISSN 1361-6544

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DOI: 10.1088/0951-7715/10/2/009

Abstract

We consider relative equilibria in symmetric Hamiltonian systems, and their persistence or bifurcation as the momentum is varied. In particular, we extend a classical result about persistence of relative equilibria from values of the momentum map that are regular for the coadjoint action, to arbitrary values, provided that either (i) the relative equilibrium is at a local extremum of the reduced Hamiltonian or (ii) the action on the phase space is (locally) free. The first case uses just point-set topology, while in the second we rely on the local normal form for (free) symplectic group actions, and then apply the splitting lemma. We also consider the Lyapunov stability of extremal relative equilibria. The group of symmetries is assumed to be compact.

Item Type:Article
Uncontrolled Keywords:Symplectic reduction, relative equilibria, momentum map
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 58 Global analysis, analysis on manifolds
MSC 2000 > 70 Mechanics of particles and systems
MIMS number:2005.37
Deposited By:Dr James Montaldi
Deposited On:12 December 2005

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