Benoist 3-流形的Bowen–Margulis测度的遍历性

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics 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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来源期刊

Journal of Modern Dynamics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including: Number theory Symplectic geometry Differential geometry Rigidity Quantum chaos Teichmüller theory Geometric group theory Harmonic analysis on manifolds. The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.