Hausdorff dimension for ergodic measures of interval exchange transformations

Jon Chaika

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arXiv · 0807.2231

Hausdorff dimension for ergodic measures of interval exchange transformations

Jon Chaika

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Abstract

I show that there exist minimal interval exchange transformations with an ergodic measure whose Hausdorff dimension is arbitrarily small, even 0. I will also show that in particular cases one can bound the Hausdorff dimension between $\frac 1 {2r+4}$ and $\frac 1 r$ for any r greater than 1.

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Jon Chaika. 2008-07-14. Hausdorff dimension for ergodic measures of interval exchange transformations. https://arxiv.org/abs/0807.2231

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