The set of uniquely ergodic IETs is path-connected

TL;DR

This paper proves that for a fixed non-degenerate permutation on at least four symbols, the set of uniquely ergodic interval exchange transformations with that permutation forms a path-connected set.

Contribution

It establishes the path-connectedness of the set of uniquely ergodic IETs for a given permutation, a new topological property in the study of IETs.

Findings

Set of uniquely ergodic IETs with fixed permutation is path-connected

Provides new insights into the topological structure of IETs

Advances understanding of ergodic properties in dynamical systems

Abstract

Let $\pi$ be a non-degenerate permutation on at least $4$ symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\pi$ is path-connected.