Journal of Modern Dynamics (JMD)

Hausdorff dimension for ergodic measures of interval exchange transformations

Pages: 457 - 464, Issue 3, July 2008      doi:10.3934/jmd.2008.2.457

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Jon Chaika - Department of Mathematics, Rice University, Houston, TX 77005, United States (email)

Abstract: 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:  interval exchange transformation, Hausdorff dimension, non-unique ergodicity.
Mathematics Subject Classification:  37A10.

Received: November 2007;      Available Online: April 2008.