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arXiv 1908.110372019-08math.DS

horocycle不变测度的测地推进极限

Limits of geodesic push-forwards of horocycle invariant measures

Giovanni Forni

备注：: 22 pages. A few misprints have been corrected, and one reference has been updated
发表信息：: Ergod. Th. Dynam. Sys. 41 (2021) 2782-2804
DOI：: 10.1017/etds.2020.87

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AI总结：

本文证明SL(2,R)作用中horocycle与geodesic子群遍历平均的条件收敛，改进测地推进弱收敛，并给出Birkhoff一般性与Oseledets正则性较弱版本的简短证明。

摘要：

我们证明了关于SL(2,R)李群在局部紧空间上的任意连续作用中horocycle和geodesic子群的遍历平均的若干一般条件收敛结果。这些结果受Eskin、Mirzakhani和Mohammadi关于SL(2,R)在Abelian微分模空间上作用的定理启发。通过我们的论证，我们可以从这些定理推导出测地流下horocycle测度推进的“弱收敛”的改进版本，以及Chaika和Eskin关于Teichmueller测地流在几乎所有方向上的Birkhoff一般性和Oseledets正则性的较弱版本定理的简短证明。

英文摘要：

We prove several general conditional convergence results on ergodic averages for horocycle and geodesic subgroups of any continuous action of the Lie group SL(2, R) on a locally compact space. These results are motivated by theorems of Eskin, Mirzakhani and Mohammadi on the SL(2,R)-action on the moduli space of Abelian differentials. By our argument we can derive from these theorems an improved version of the "weak convergence" of push-forwards of horocycle measures under the geodesic flow and a short proof of weaker versions of theorems of Chaika and Eskin on Birkhoff genericity and Oseledets regularity in almost all directions for the Teichmueller geodesic flow.

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