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2010.95: On the stability of Hamiltonian relative equilibria with non-trivial isotropy

2010.95: James Montaldi and Miguel Rodriguez-Olmos (2010) On the stability of Hamiltonian relative equilibria with non-trivial isotropy.

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Abstract

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subalgebra of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant.

Item Type:MIMS Preprint
Uncontrolled Keywords:Hamiltonian systems, symmetry, stability
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 53 Differential geometry
MIMS number:2010.95
Deposited By:Dr James Montaldi
Deposited On:08 November 2010

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