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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

Jon Chaika 1,

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.
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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