Centralizers of hyperbolic and kinematic-expansive flows

2019/03/26 by Bakker, Lennard, Fisher, Todd, Hasselblatt, Boris
#37C10 #37C20 #37D20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.10948

Abstract

We show generic C^∞ hyperbolic flows (Axiom A and no cycles, but not transitive Anosov) commute with no C^∞-diffeomorphism other than a time-t map of the flow itself. Kinematic expansivity, a substantial weakening of expansivity, implies that C⁰ flows have quasi-discrete C⁰-centralizer, and additional conditions broader than transitivity then give discrete C⁰-centralizer. We also prove centralizer-rigidity: a diffeomorphism commuting with a generic hyperbolic flow is determined by its values on any open set.

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