Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Persistence of stationary motion under explicit symmetry breaking
  perturbation   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.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: patt-sol