Persistence of stationary motion under explicit symmetry breaking perturbation

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 equivariant Hamiltonian systems. A lower bound for the number of orbits of equilibria and orbits of relative equilibria which persist after a small perturbation is given. This bound is given in terms of the equivariant Lyusternik-Schnirelmann category of the group orbit.

25 pages, 4 figures

References in corpus (2)

• The Dynamics of a Rigid Body in Potential Flow with Circulation
• Symplectic slice for subgroup actions

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