# American Institute of Mathematical Sciences

July  2008, 2(3): 457-464. doi: 10.3934/jmd.2008.2.457

## Hausdorff dimension for ergodic measures of interval exchange transformations

 1 Department of Mathematics, Rice University, Houston, TX 77005, United States

Received  November 2007 Published  April 2008

We show that there exist minimal interval-exchange transformations with an ergodic measure whose Hausdorff dimension is arbitrarily small, even 0. We 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.
Citation: Jon Chaika. Hausdorff dimension for ergodic measures of interval exchange transformations. Journal of Modern Dynamics, 2008, 2 (3) : 457-464. doi: 10.3934/jmd.2008.2.457
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