التفاصيل البيبلوغرافية
| العنوان: |
Exceptional directions for the Teichm¨ uller geodesic flow and Hausdorff dimension. |
| المؤلفون: |
Al-Saqban, Hamid, Apisa, Paul, Erchenko, Alena, Khalil, Osama, Mirzadeh, Shahriar, Uyanik, Caglar |
| المصدر: |
Journal of the European Mathematical Society (EMS Publishing); 2021, Vol. 23 Issue 5, p1423-1476, 54p |
| مصطلحات موضوعية: |
FRACTAL dimensions, PERMUTATIONS, ERGODIC theory, GEODESICS, BIRKHOFF'S theorem (Relativity) |
| مستخلص: |
We prove that for every flat surface ω, the Hausdorff dimension of the set of directions in which Teichmüller geodesics starting from ω exhibit a definite amount of deviation from the correct limit in Birkhoff's and Oseledets' Theorems is strictly less than 1. This theorem extends a result by Chaika and Eskin where they proved that such sets have measure 0. We also prove that the Hausdorff dimension of the directions in which Teichmüller geodesics diverge on average in a stratum is bounded above by 1/2, strengthening a classical result due to Masur. Moreover, we show that the Hausdorff codimension of the set of non-weakly mixing IETs with permutation (d,d-1,...,1), where d is an odd number, is exactly 1/2 and strengthen a result by Avila and Leguil. [ABSTRACT FROM AUTHOR] |
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