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Stable sets and mean Li–Yorke chaos in positive entropy actions of bi-orderable amenable groups

Published online by Cambridge University Press:  01 June 2015

WEN HUANG  and
LEI JIN
WEN HUANG
Affiliation:
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, PR China Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China email wenh@mail.ustc.edu.cn
LEI JIN
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China email jinleim@mail.ustc.edu.cn
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Abstract

It is proved that positive entropy implies mean Li–Yorke chaos for a $G$ -system, where $G$ is a countable, infinite, discrete, bi-orderable amenable group. Examples are given for the cases of integer lattice groups and groups of integer unipotent upper triangular matrices.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 8 , December 2016 , pp. 2482 - 2497
Copyright
© Cambridge University Press, 2015 

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