SMOOTH RIGIDITY FOR CODIMENSION ONE ANOSOV FLOWS

Andrey Gogolev, Federico Rodriguez Hertz

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Abstract

We introduce the matching functions technique in the setting of Anosov flows. Then we observe that simple periodic cycle functionals (also known as temporal distances) provide a source of matching functions for conjugate Anosov flows. For conservative codimension one Anosov flows ϕt : M Ñ M, dim M ě 4, these simple periodic cycle functionals are C1 regular and, hence, can be used to improve regularity of the conjugacy. Specifically, we prove that a continuous conjugacy must, in fact, be a C1 diffeomorphism for an open and dense set of codimension one conservative Anosov flows.

Original languageEnglish (US)
Pages (from-to)2975-2988
Number of pages14
JournalProceedings of the American Mathematical Society
Volume151
Issue number7
DOIs
StatePublished - Jul 1 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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