Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

被引：18

作者：

Climenhaga, Vaughn ^{[1
]}

Knieper, Gerhard ^{[2
]}

War, Khadim ^{[3
]}

机构：

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Ruhr Univ Bochum, Dept Math, D-44780 Bochum, Germany

[3] IMPA, Estr Dona Castorina 110, Rio De Janeiro, Brazil

来源：

ADVANCES IN MATHEMATICS | 2021年 / 376卷

关键词：

Geodesic flows without conjugate points; Measure of maximal entropy; EQUILIBRIUM STATES; TOPOLOGICAL-ENTROPY; RESIDUAL FINITENESS; SURFACE; GROWTH; DYNAMICS;

D O I：

10.1016/j.aim.2020.107452

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for closed surfaces M with Riemannian metrics without conjugate points and genus >= 2 the geodesic flow on the unit tangent bundle (TM)-M-1 has a unique measure of maximal entropy. Furthermore, this measure is fully supported on (TM)-M-1, is the limiting distribution of closed orbits, and the flow is mixing with respect to this measure. We formulate conditions under which this result extends to higher dimensions. (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：44

共 52 条

[1]

[Anonymous], 1998, Grad. Texts in Math.

[2]

Arzhantseva G., 2014, TRENDS MATH RES PERS, V1, P7

[3] On the mixing property for hyperbolic systems [J].