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

• 成果类型: Article
• 署名作者: Chaika, Jon; Masur, Howard
• 署名单位: Utah System of Higher Education; University of Utah; University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00978-3
• 发表日期: 2020
• 页码: 749-832
• 关键词: dimension; transformations

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.