The Hopf–Tsuji–Sullivan dichotomy in higher rank and applications to Anosov subgroups

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2021-05-28 DOI:10.3934/jmd.2023008

M. Burger, Or Landesberg, Minju M. Lee, H. Oh

引用次数: 38

Abstract

We establish an extension of the Hopf-Tsuji-Sullivan dichotomy to any Zariski dense discrete subgroup of a semisimple real algebraic group $G$. We then apply this dichotomy to Anosov subgroups of $G$, which surprisingly presents a different phenomenon depending on the rank of the ambient group $G$.

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高秩的Hopf–Tsuji–Sullivan二分法及其在Anosov子群中的应用

我们将Hopf-Tsuji-Slivan二分法推广到半单实代数群$G$的任何Zariski稠密离散子群。然后，我们将这种二分法应用于$G$的Anosov子群，令人惊讶的是，根据环境群$G$$的秩，它呈现出不同的现象。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.