Centralizers of hyperbolic and kinematic-expansive flows
Mathematics Research Reports, Volume 2 (2021), pp. 21-44.

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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DOI: 10.5802/mrr.8
Classification: 37D20,  37C10,  37C20
Keywords: Dynamical systems; flows; commuting; expansive; hyperbolic
Lennard Bakker 1; Todd Fisher 1; Boris Hasselblatt 2

1 Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
2 Department of Mathematics, Tufts University, Medford, MA 02144, USA
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Lennard Bakker; Todd Fisher; Boris Hasselblatt. Centralizers of hyperbolic and kinematic-expansive flows. Mathematics Research Reports, Volume 2 (2021), pp. 21-44. doi : 10.5802/mrr.8. https://mrr.centre-mersenne.org/articles/10.5802/mrr.8/

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