Hölder翻译流谱的规律性

A. Bufetov, B. Solomyak
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引用次数: 11

摘要

本文研究了任意格$g\ g_2 $平面上对应于阿贝尔微分的一般平移流。根据Avila-Forni定理,这些气流是弱混合的。在我们的论文[10,12]中,我们建立了这些流的光谱测量的H\ ' old性质。最近,受[10]的启发,Forni[17]获得了任意属表面的光谱测度的H\ \ old估计。在这里,我们将Forni的思想与[10]的符号方法结合起来,并证明了随机马尔可夫压缩上流的谱测度的H\ \ older正则性,特别是对于所有类型的平移流。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hölder regularity for the spectrum of translation flows
The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus $g\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. In genus 2, the H\"older property for the spectral measures of these flows was established in our papers [10,12]. Recently Forni [17], motivated by [10], obtained H\"older estimates for spectral measures in the case of surfaces of arbitrary genus. Here we combine Forni's idea with the symbolic approach of [10] and prove H\"older regularity for spectral measures of flows on random Markov compacta, in particular, for translation flows in all genera.
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