Bowen Entropy And Weighted Pressure For Fixed-point Free Flows

In this paper,we consider reparametrizations of the flows,and study the rela-tionship between Bowen topological entropy and measure-theoretic entropy for flows without fixed points,we obtain a variational principle and establish the Brin-Katok's entropy formula for flows without fixed points in non-ergodic case.Secondly,we gen-eralize the weighted topological entropy to the weighted topological pressure,define the weighted topological pressure for flows on non-compact subsets and the one of its time-one map,explore the relationship between them.This paper is organized as follows:In Chapter 1,we introduce the backgrounds of topological entropy,topological pressure,Bowen topological entropy and measure-theoretic entropy and the basic knowledge of weighted entropy for flows as well as the main results of this thesis.In Chapter 2,by considering reparametrizations of the flows without fixed points,we prove the Brin-Katok's entropy formula for flows in non-ergodic case,and give a proof of the variational principle between the Bowen topological entropy of the set of generic points of ? and the measure-theoretic entropy with respect to? in ergodic case.In Chapter 3,we construct the relationship between the weighted topological pressure for flows on non-compact sets and the one of its time-one map.