The set of non-uniquely ergodicd-IETs has Hausdorff codimension 1/2

摘要

We show that the set of not uniquely ergodic d-IETs with permutation in the Rauzy class of the hyperelliptic permutation has Hausdorff dimension d - 3/2 [in the (d - 1)-dimension space of d-IETs] for d >= 5. For d = 4 this was shown by Athreya-Chaika and for d is an element of {2, 3} the set is known to have dimension d - 2. This provides lower bounds on the Hausdorff dimension of non-weakly mixing IETs and, with input from Al-Saqban et al. (Exceptional directions for the Teichmuller geodesic flow and Hausdorff dimension, 2017. arXiv:1711.10542), identifies the Hausdorff dimension of non-weakly mixing IETs with permutation (d, d - 1, ..., 2, 1) when d is odd.