Mean Li-Yorke Chaos And Mean Dimension For Amenable Group Actions

It is well known that mean Li-Yorke chaos and mean dimension are important issues.In this essay,we mainly study mean Li-Yorke chaos along some good se-quences,multivariant,mean Li-Yorke chaos for countable amenable group actions,and conditional mean dimension with potential.The thesis is organized as follows:In chapter 1,we introduce countable bi-orderable amenable group,mean Li-Yorke chaos,mean dimension as well as the main results of this thesis.In chapter 2,we study mean Li-Yorke chaos along some good sequences,and prove that the positive relative entropy implies sequence chaos.In chapter 3,we study multivariant mean Li-Yorke chaos for countable amenable group actions,and prove that there is this chaos in positive entropy actions.In chapter 4,we study the properties of mean dimension with potential and conditional mean dimension with potential,and obtain an inequality to estimate the mean dimension with potential of an extension system.