Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces
Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces
复制标题
区间交换映射空间和平动面空间上Teichmüller流的递推统计
DOI：
10.1214/16-aihp758
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发表时间：
2013
影响因子：
1.5
通讯作者：
M. Todd
中科院分区：
文献类型：
--
作者：
R. Aimino;M. Nicol;M. Todd
本文证明了作用在拟Holder函数空间上的Rauzy-Veech-Zorich重整化映射的转移算子是拟紧的，并导出了该映射及其Teichmuller流的某些统计递归性质.我们建立Borel-Cantelli引理，极值统计和返回时间统计的地图和流。以前的结果已经在保持器或解析函数空间中建立了拟紧性，例如M. Pollicott和T.森田准Holder函数空间对于研究返回时间统计特别有用。特别地，我们在Teichmuller流的背景下建立了嵌套球的收缩目标性质。我们的观点、方法和术语来自M. Pollicott增加了M。维亚纳。
In this note we show that the transfer operator of a Rauzy-Veech-Zorich renormalization map acting on a space of quasi-Holder functions is quasicompact and derive certain statistical recurrence properties for this map and its associated Teichmuller flow. We establish Borel-Cantelli lemmas, Extreme Value statistics and return time statistics for the map and flow. Previous results have established quasicom-pactness in Holder or analytic function spaces, for example the work of M. Pollicott and T. Morita. The quasi-Holder function space is particularly useful for investigating return time statistics. In particular we establish the shrinking target property for nested balls in the setting of Teichmuller flow. Our point of view, approach and terminology derive from the work of M. Pollicott augmented by that of M. Viana.
DOI：
10.1090/s0002-9947-08-04520-0
发表时间：
2008-01-01
影响因子：
1.3
作者：
Melbourne, Ian;Nicol, Matthew
通讯作者：
Nicol, Matthew