Fontaine, Marine and Montaldi, James
(2019)
*Persistence of stationary motion under explicit symmetry breaking perturbation.*
Nonlinearity, 32 (6).
pp. 1999-2023.

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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: | Article |
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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: | 06 May 2019 11:07 |

Last Modified: | 06 May 2019 11:07 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2706 |

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