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Accessibility and centralizers for partially hyperbolic flows

Published online by Cambridge University Press:  11 May 2021

TODD FISHER*
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT84602, USA
BORIS HASSELBLATT
Affiliation:
Department of Mathematics, Tufts University, Medford, MA02144, USA (e-mail: [email protected])

Abstract

Stable accessibility of partially hyperbolic systems is central to their stable ergodicity, and we establish its $C^1$ -density among partially hyperbolic flows, as well as in the categories of volume-preserving, symplectic, and contact partially hyperbolic flows. As applications, we obtain on one hand in each of these four categories of flows the $C^1$ -density of the $C^1$ -stable topological transitivity and triviality of the centralizer, and on the other hand the $C^1$ -density of the $C^1$ -stable K-property of the natural volume in the latter three categories.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

To the memory of Anatole Katok

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