TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS

被引：0

作者：

Burguet, David ^{[1
]}

Shi, Ruxi ^{[2
]}

机构：

[1] Univ Picardie Jules Verne, CNRS, F-80000 Amiens, France

[2] Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200438, Peoples R China

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 378卷 / 05期

关键词：

DYNAMICS;

D O I：

10.1090/tran/9407

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

. For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak-& lowast; topology has infinite topological mean dimension. As an application, it answers a question of Kloeckner [J. Topol. Anal. 4 (2012), pp. 203-235]. We also estimate the rate of divergence of the entropy with respect to the Wasserstein distance when the scale goes to zero.

引用

页码：3085 / 3103

页数：19