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.

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Keywords: Dynamical systems; flows; commuting; expansive; hyperbolic

^{1}; Fisher, Todd

^{1}; Hasselblatt, Boris

^{2}

@article{MRR_2021__2__21_0, author = {Bakker, Lennard and Fisher, Todd and Hasselblatt, Boris}, title = {Centralizers of hyperbolic and kinematic-expansive flows}, journal = {Mathematics Research Reports}, pages = {21--44}, publisher = {MathOA foundation}, volume = {2}, year = {2021}, doi = {10.5802/mrr.8}, language = {en}, url = {http://www.numdam.org/articles/10.5802/mrr.8/} }

TY - JOUR AU - Bakker, Lennard AU - Fisher, Todd AU - Hasselblatt, Boris TI - Centralizers of hyperbolic and kinematic-expansive flows JO - Mathematics Research Reports PY - 2021 SP - 21 EP - 44 VL - 2 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/mrr.8/ DO - 10.5802/mrr.8 LA - en ID - MRR_2021__2__21_0 ER -

%0 Journal Article %A Bakker, Lennard %A Fisher, Todd %A Hasselblatt, Boris %T Centralizers of hyperbolic and kinematic-expansive flows %J Mathematics Research Reports %D 2021 %P 21-44 %V 2 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/mrr.8/ %R 10.5802/mrr.8 %G en %F MRR_2021__2__21_0

Bakker, Lennard; Fisher, Todd; Hasselblatt, Boris. Centralizers of hyperbolic and kinematic-expansive flows. Mathematics Research Reports, Volume 2 (2021), pp. 21-44. doi : 10.5802/mrr.8. http://www.numdam.org/articles/10.5802/mrr.8/

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