THE UNIQUE MEASURE OF MAXIMAL ENTROPY FOR A COMPACT RANK ONE LOCALLY CAT(0) SPACE

被引：4

作者：

Ricks, Russell ^{[1
]}

机构：

[1] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2021年 / 41卷 / 02期

关键词：

Entropy; nonpositive curvature; geodesic flows;

D O I：

10.3934/dcds.2020266

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank one axis. We prove the Bowen-Margulis measure on the space of geodesics is the unique measure of maximal entropy for the geodesic flow, which has topological entropy equal to the critical exponent of the Poincare series.

引用

页码：507 / 523

页数：17

共 3 条

[1] Counting closed geodesics in a compact rank-one locally CAT(0) space
Ricks, Russell
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2022, 42 (03) : 1220 - 1251
[2] Mixing rank-one actions of locally compact Abelian groups
Danilenko, Alexandre I.
Silva, Cesar E.
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2007, 43 (04): : 375 - 398
[3] On regular CAT(0) cube complexes and the simplicity of automorphism groups of rank-one CAT(0) cube complexes
Lazarovich, Nir
COMMENTARII MATHEMATICI HELVETICI, 2018, 93 (01) : 33 - 54

← 1 →