Pressure For Flows Without Fixed Points

It is well known that measure-theoretic entropy and topological entropy aRe two important concepts of dynamical systens.The relationship between these two quantities is called variational principle.And pressure is a natural generalization of entropy.In this thesis,we study topological pressure,measure-theoretic pressure for flows without fixed points.We obtain a variational principle and a Katok's entropy formula of pressure version.The thesis is organized as follows:In Chapter 1,we introduce the backgrounds of topological entropy,topological pressure and some classical results as well as the main results of this thesis.In Chapter 2,by considering all possible reparametrizations of the flows in-stead of the time 1 maps,we define Pesin-Pitskel topological pressure and measure-theoretic pressure for flows.Then we study the relationship between Pesin-Pitskel topological pressure on an arbitrary subset and measure-theoretic pressure of Borel probability measures.In Chapter 3,we give a new definition of measure-theoretic pressure for ergodic measures and establish a Katok's entropy formula of pressure version.Moreover,we prove a variational principle between Pesin-Pitskel topological pressure and measure-theoretic pressure of ergodic measures.Additionally,we get the result that the Pesin-Pitskel topological pressure defined here is equivalent to the one defined in[26].