Tail Pressures For Sub-additive Potentials

This thesis studies the topological tail pressure for sub-additive potentials in topological dynamical systems.We mainly define the topological tail pressure and measure-theoretic tail pressure for sub-additive potentials,and some properties of them are obtained.The variational principle is proved under certain conditions.This thesis includes the following there parts.In the first part,we review the basis concepts and results in dynamical system,especially the concepts of tail entropy and tail pressure.And then we introduce the background and purpose of this study.The main content in second part is the variational principle.More precisely,we give some definitions of the topological tail pressure for sub-additive potentials and prove that they are equivalent if the potentials are continuous.And then we prove the main result of this thesis: the variational principle for sub-additive potential under a certain condition.It exhibits the relationship between topological tail pressure and measure-theoretic tail entropy.In the last part of this thesis,we define a new measure-theoretic tail pressure for invariant measures of sub-additive potentials on a compact metric space and some properties of it are obtained.The main result of this part is Theorem 5.1.