Topological Entropy And Average Dimension Under The Average Metric

This thesis is divided into four parts.We study topological entropy,topological pressure with average metric and metric mean dimension with r metric.This thesis is organized as follows:In chapter 1,we introduce the backgrounds of topological entropy,topologi-cal pressure,metric mean dimension and the basic knowledge of mistake function,average metric.In chapter 2,we explore the properties and the variational principle of topolog-ical entropy with average metric.In chapter 3,we show the topological pressure of arbitrary subset with average metric is equal to the topological pressure of the subset.In chapter 4,we show the mean dimension with r metric is equal to the mean dimension with Bowen metric.