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arXiv · 2007.04352

Accessibility and centralizers for partially hyperbolic flows

Todd Fisher·Boris Hasselblatt
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Abstract

Stable accessibility for partially hyperbolic diffeomorphisms is central to their ergodic theory, and we establish its \(C^1\)-density among 1. all, 2. volume-preserving, 3. symplectic, and 4. contact partially hyperbolic flows. As applications, we obtain in each of these 4 categories \(C^1\)-density of \(C^1\)-stable topological transitivity, ergodicity, and triviality of the centralizer.

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Todd Fisher, Boris Hasselblatt. 2020-07-08. Accessibility and centralizers for partially hyperbolic flows. https://doi.org/10.1017/etds.2021.24

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