Centralizers of hyperbolic and kinematic-expansive flows

Bakker, Lennard; Fisher, Todd; Hasselblatt, Boris

Mathematics Research Reports, Tome 2 (2021), pp. 21-44.

We show that generic $C^{\infty }$ hyperbolic flows commute with no $C^{\infty }$-diffeomorphism other than a time-$t$ map of the flow itself. Kinematic-expansivity, a substantial weakening of expansivity, implies that $C^0$ flows have quasidiscrete $C^0$-centralizer, and additional conditions broader than transitivity then give discrete $C^0$-centralizer. We also prove centralizer-rigidity: a diffeomorphism commuting with a generic hyperbolic flow is determined by its values on any open set.

Classification : 37D20, 37C10, 37C20
Mots clés : Dynamical systems; flows; commuting; expansive; hyperbolic

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