Stability of interval translation maps is characterized by absence of critical connections and matching.
Duke Math
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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.
Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.
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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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Isomoprhism of generalized Bratteli diagrams
Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.