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.
Dynamics of piecewise isometries
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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.