Accessibility and centralizers for partially hyperbolic flows

Abstract

AbstractStable 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.