Abstract
We show that generic C ∞ hyperbolic flows commute with no C ∞ -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.
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