Benoist 3-流形的Bowen–Margulis测度的遍历性

Pub Date : 2017-05-23 DOI:10.3934/jmd.2020011

Harrison Bray

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引用次数: 8

摘要

我们研究了Benoist引入的一类3-流形的测地流，这些流形具有一定的双曲性，但不是黎曼的，不是CAT（0）的，并且具有非C^1测地流。几何是三维的非严格凸Hilbert几何，它通过离散的投影变换群接纳紧致商流形。我们证明了Patterson-Slivan密度是正则的，并将其应用于计数，并明确构造了最大熵的Bowen-Margulis测度。这项工作的主要结果是Bowen-Margulis测度的遍历性。

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Ergodicity of Bowen–Margulis measure for the Benoist 3-manifolds

We study the geodesic flow of a class of 3-manifolds introduced by Benoist which have some hyperbolicity but are non-Riemannian, not CAT(0), and with non-C^1 geodesic flow. The geometries are nonstrictly convex Hilbert geometries in dimension three which admit compact quotient manifolds by discrete groups of projective transformations. We prove the Patterson-Sullivan density is canonical, with applications to counting, and construct explicitly the Bowen-Margulis measure of maximal entropy. The main result of this work is ergodicity of the Bowen-Margulis measure.

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