On the Hausdorff Dimension of Measures for a Non-Uniquely Ergodic Family of Interval Exchange Transformations

Abstract: In this paper, based on a construction by J. Fickenscher, we construct a family of non-uniquely ergodic interval exchange transformations on $n$ intervals with the maximal possible number of measures, $\left\lfloor \frac{n}{2} \right\rfloor$. Subsequently, we generalize J. Chaika's result on estimating the Hausdorff dimension of the two measures from M. Keane's example to the family of interval exchange transformations with the maximal possible number of measures.