Weighted Topological Entropy For Fixed-point-free Flows

In this thesis,we study the weighted Bowen entropy and weighted measure-theoretic entropy of flows,then we establish the variational principle between them.By establishing the weighted Brin-Katok entropy formula of flows in ergodic case,we prove the weighted Bowen entropy is equal to weighted topological entropy for flows on the whole compact metric space.Finally,we give the weighted Katok entropy formula of flows.The thesis is organized as follows:In Chapter 1,we introduce the backgrounds of topological entropy and measure-theoretic entropy of flows as well as the main results of this thesis.In Chapter 2,we define the weighted Bowen entropy and measuretheoretic entropy of flows.We introduce some properties about weighted reparametrization balls and prove a variational principle of weighted entropy of flows.In Chapter 3,we establish the weighted Brin-Katok entropy formula of flows,and prove the weighted Bowen entropy on the whole compact metric space is equal to the weighted topological entropy.In Chapter 4,we introduce a definition of weighted measuretheoretic entropy and prove the weighted Katok entropy formula of flows.