Symmetric periodic orbits in families of interval exchange maps persist for small perturbations and are found via one-dimensional searches along symmetry lines, with bifurcations connected to the standard map viewed as a two-interval case.
Time-reversal symmetry in dynamical systems: A survey
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Comet-type periodic orbits exist in the CR3BP and undergo vertical self-resonant bifurcations up to multiplicity six in the Earth-Moon system.
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Perturbed Families of Symmetric Interval Exchange Maps
Symmetric periodic orbits in families of interval exchange maps persist for small perturbations and are found via one-dimensional searches along symmetry lines, with bifurcations connected to the standard map viewed as a two-interval case.