Weighted Bowen Entropy And Topological Pressure For Fixed-point-free Flows

In this thesis,we study the topological entropy and topological pressure for fixed-point free flows by using the reparameterizations of time.We define the weighted Bowen entropy and measure-theoretic entropy for fixed-point free flows on compact metric space,and prove the weighted Bowen entropy of sets of generic points of ergodic measure is equal to the weighted measure-theoretic entropy with respect to .In addition,we introduce the concept of non-additive topological pressure,and prove the variational principle of non-additive pressure for fixed-point free flows.This thesis is organized as follows:In Chapter 1,we introduce the backgrounds of measure-theoretic entropy,topological entropy and topological pressure.Moreover,we give the main results of this thesis.In Chapter 2,by giving the weighted Brin-Katok entropy formula for non-ergodic measure,we prove the weighted Bowen entropy of sets of generic points of ergodic measure is equal to the weighted measure-theoretic entropy with respect to ,and show a Billingsley type Theorem for weighted Bowen entropy.In Chapter 3,we introduce the non-additive topological pressure,and establish a variational principle of non-additive topological pressure for fixed-point free flows.