Hamiltonian relative equilibria with continuous isotropy

Montaldi, James and Rodriguez-Olmos, Miguel (2015) Hamiltonian relative equilibria with continuous isotropy. [MIMS Preprint]

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In symmetric Hamiltonian systems, relative equilibria usually arise in continuous families. The geometry of these families in the setting of free actions of the symmetry group is well-understood. Here we consider the question for non-free actions. Some results are already known in this direction, and we use the so-called bundle equations to provide a systematic treatment of this question which both consolidates the known results, extending the scope of the results to deal with non-compact symmetry groups, as well as producing new results. Specifically we address questions about the stability, persistence and bifurcations of these relative equilibria.

Item Type: MIMS Preprint
Uncontrolled Keywords: Hamiltonian systems, momentum map, bifurcations, persistence
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User: Dr James Montaldi
Date Deposited: 15 Dec 2015
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2422

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