Hausdorff dimension for ergodic measures of interval exchange transformations

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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

Abstract
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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.

Keywords: non-unique ergodicity., Hausdorff dimension, interval exchange transformation.

Mathematics Subject Classification: 37A1.

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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