Accessibility and ergodicity for collapsed Anosov flows

TL;DR

This paper proves that a broad class of partially hyperbolic diffeomorphisms are ergodic under volume preservation unless they contain a su-torus, confirming a conjecture for these systems.

Contribution

It establishes accessibility and ergodicity for a large class of partially hyperbolic diffeomorphisms, extending known results and confirming a conjecture.

Findings

Non-wandering systems are accessible unless containing a su-torus.

Accessible systems preserve volume and are ergodic.

Confirms the Hertz-Hertz-Ures conjecture for this class.

Abstract

We consider a class of partially hyperbolic diffeomorphisms introduced in [BFP] which is open and closed and contains all known examples. If in addition the diffeomorphism is non-wandering, then we show it is accessible unless it contains a su-torus. This implies that these systems are ergodic when they preserve volume, confirming a conjecture by Hertz-Hertz-Ures for this class of systems.