On the Hausdorff dimensions of a singular ergodic measure for some minimal interval exchange transformations

TL;DR

This paper investigates the Hausdorff dimensions of specific minimal, non-uniquely ergodic interval exchange transformations, revealing how typical points for different measures can approximate each other in distinct ways.

Contribution

It provides new results on the Hausdorff dimension of ergodic measures in minimal interval exchange transformations and explores the approximation behavior of typical points.

Findings

Hausdorff dimensions of certain minimal non-uniquely ergodic IETs analyzed

Typical points for different ergodic measures can approximate each other differently

New insights into the geometric structure of ergodic measures in IETs

Abstract

We show some results about the Hausdorff dimension of particular minimal but not uniquely ergodic interval exchange transformations. There is an appendix which shows that typical points for two different ergodic measures of an interval exchange can approximate each other differently.