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

Montaldi, James and Rodriguez-Olmos, Miguel (2010) On the stability of Hamiltonian relative equilibria with non-trivial isotropy. [MIMS Preprint]

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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 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
Depositing User:	Dr James Montaldi
Date Deposited:	08 Nov 2010
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1538

Available Versions of this Item

• On the stability of Hamiltonian relative equilibria with non-trivial isotropy. (deposited 08 Nov 2010) [Currently Displayed]
  • On the stability of Hamiltonian relative equilibria with non-trivial isotropy. (deposited 20 Jul 2011)

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