On the Hausdorf Dimension of Minimal Interval Exchange Transformations with Flips

TL;DR

This paper establishes linear bounds for the Hausdorff dimension of minimal interval exchange transformations with flips, providing insights into their geometric complexity and ergodic properties.

Contribution

It introduces linear bounds for the Hausdorff dimension of minimal interval exchange transformations with flips, advancing understanding of their fractal geometry.

Findings

Linear upper and lower bounds for the Hausdorff dimension of these transformations

Linear lower bound for the dimension of non-uniquely ergodic transformations

Insights into the structure of minimal interval exchange transformations with flips

Abstract

We prove linear upper and lower bounds for the Hausdorff dimension set of minimal interval exchange transformations with flips (in particular without periodic points), and a linear lower bound for the Hausdorff dimension of the set of non-uniquely ergodic minimal interval exchange transformations with flips.