Hausdorff dimension for ergodic measures of interval exchange transformations

Details Hausdorff dimension for ergodic measures of interval exchange transformations Hausdorff dimension for ergodic measures of interval exchange transformations

2008-07-14

arxiv.org/abs/0807.2231v1

Journal of Modern Dynamics, July 2008 455-462

Mathematics

Dynamical Systems

7 pages

Scientific paper

I show that there exist minimal interval exchange transformations with an
ergodic measure whose Hausdorff dimension is arbitrarily small, even 0. I 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.

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