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Accessibility and centralizers for partially hyperbolic flows
Ergodic Theory and Dynamical Systems ( IF 0.8 ) Pub Date : 2021-05-11 , DOI: 10.1017/etds.2021.24
TODD FISHER 1 , BORIS HASSELBLATT 2
Affiliation  

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.

中文翻译:

部分双曲线流的可访问性和集中器

部分双曲线系统的稳定可达性是其稳定遍历性的核心,我们建立了它的$C^1$- 部分双曲线流动之间的密度,以及保体积、辛和接触部分双曲线流动类别中的密度。作为应用程序,我们一方面在这四类流中的每一类中获得$C^1$- 密度$C^1$-中心化器的稳定拓扑传递性和平凡性,另一方面$C^1$- 密度$C^1$- 后三类自然体积的稳定 K 属性。
更新日期:2021-05-11
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