Ergodicity of $C^2$ minimal actions of Thompson group $T$ on the circle

TL;DR

This paper proves that all $C^2$ minimal actions of Thompson group $T$ on the circle are ergodic with respect to Lebesgue measure, and non-minimal actions have negligible minimal sets.

Contribution

It establishes ergodicity for $C^2$ minimal actions of Thompson group $T$ on the circle, a novel result in the dynamics of this group.

Findings

All $C^2$ minimal actions are ergodic with respect to Lebesgue measure.

Non-minimal actions have minimal sets of Lebesgue measure zero.

Abstract

We show that every $C^2$ minimal action of Thompson group $T$ on the circle is ergodic with respect to the Lebesgue measure. If such action is not minimal then the Lebesgue measure of the exceptional minimal set is zero.