Persistence of stationary motion under explicit symmetry breaking perturbation

Fontaine, Marine and Montaldi, James (2018) Persistence of stationary motion under explicit symmetry breaking perturbation. [MIMS Preprint]

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Abstract

Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed in a way that the perturbation preserves only some symmetries of the original system. We give a geometric approach to study this phenomenon in the setting of Hamiltonian systems. We provide a method for determining the equilibria and relative equilibria that persist after a symmetry breaking perturbation. In particular a lower bound for the number of each is found, in terms of an equivariant Lyusternik-Schnirelmann category of the group orbit.

Item Type: MIMS Preprint
Uncontrolled Keywords: Symmetry breaking, Hamiltonian systems, Lie group actions
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: 13 May 2018 09:45
Last Modified: 13 May 2018 09:45
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2643

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