Stability of interval translation maps is characterized by absence of critical connections and matching.
Gauss measures for transformations on the space of interval exchange maps
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A transversality theorem is proved for dynamically defined vector subspaces of interval translation maps, yielding a perturbation result that controls first-return dynamics while preserving global behavior.
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.
citing papers explorer
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Characterisation of Stability for Interval Translation Maps
Stability of interval translation maps is characterized by absence of critical connections and matching.
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Transversality for Interval Translation Maps
A transversality theorem is proved for dynamically defined vector subspaces of interval translation maps, yielding a perturbation result that controls first-return dynamics while preserving global behavior.
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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.