Stability of interval translation maps is characterized by absence of critical connections and matching.
Interval exchange transformations and measured foliations
4 Pith papers cite this work. Polarity classification is still indexing.
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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.
Conjecture that simple geodesics on finite modular covers have transcendental or algebraic endpoints, proved for minimal laminations.
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.