Accessibility and centralizers for partially hyperbolic flows

TL;DR

This paper proves that stable accessibility is dense in various classes of partially hyperbolic flows, leading to generic properties like ergodicity and trivial centralizers, advancing understanding in dynamical systems.

Contribution

It establishes the C^1-density of stable accessibility for multiple classes of partially hyperbolic flows, a key step in ergodic theory.

Findings

C^1-density of stable accessibility in all four categories

Density of C^1-stable topological transitivity

Density of ergodicity and trivial centralizer

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.