On the ergodic properties of time changes of partially hyperbolic homogeneous flows

TL;DR

This paper proves that smooth time changes of accessible partially hyperbolic homogeneous flows are K-systems and mixing of all orders, and establishes stable ergodicity for their time-one maps.

Contribution

It demonstrates that all smooth time changes of these flows are K-systems and mixing of all orders, and proves stable ergodicity for their time-one maps.

Findings

All smooth time changes are K-systems and mixing of all orders.

Stable ergodicity is established for the time-one map of these flows.

The results apply to accessible partially hyperbolic homogeneous flows.

Abstract

For any accessible partially hyperbolic homogeneous flow, we show that all smooth time changes are K and hence mixing of all orders. We also establish stable ergodicity for time-one map of these time changes.