Affine interval exchange transformations with flips and wandering intervals

TL;DR

This paper explores a special class of affine interval exchange transformations with flips, demonstrating the existence of uniquely ergodic systems with wandering intervals and Cantor set supports.

Contribution

It introduces new examples of affine interval exchange transformations with flips that exhibit unique ergodicity and wandering intervals, expanding understanding of their dynamical properties.

Findings

Existence of uniquely ergodic affine IETs with flips and wandering intervals

Supports of invariant measures can be Cantor sets in these systems

Provides constructions demonstrating these properties

Abstract

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor set.