Persistence of stationary motion under explicit symmetry breaking perturbation

Marine Fontaine, James Montaldi

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    Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed to a system which has strictly less symmetry. 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.
    Original languageEnglish
    Pages (from-to)1999-2023
    Number of pages25
    Issue number6
    Early online date3 May 2019
    Publication statusPublished - 3 May 2019


    • Symmetry breaking
    • Hamiltonian systems with symmetry
    • Lie group actions


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