Smooth rigidity for codimension one Anosov flows

2021/12/02 by Gogolev, Andrey, Hertz, Federico Rodriguez
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.01595

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 distance functions) provide a source of matching functions for conjugate Anosov flows. For conservative codimension one Anosov flows φ^t\colon M→ M, dim M≥ 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.

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