Hausdorff dimension for ergodic measures of interval exchange transformations
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.
Received: November 2007; Available Online: April 2008. |