The Sequence Pressure On Compact Metric Space

Topological dynamical system is an important branch in dynamical system,and entropy describes the complexity of the system.Topological pressure is a further extension of topological entropy.In this paper,we mainly discuss the case of(X,d)which is compact metric space,T:X(?)X is continuous map on X,besides A=(t _i:i=1,2,3···) is integer sequence.The first part,we consider the extension of sequence entropy to sequence pressure,and give several equivalent definitions of sequence pressure.The second part studies some properties of sequence pressure.The third part discusses the classical variational principle of sequence pressure and the relationship between sequence pressure and topological pressure,measure-theoretical pressure.The specific arrangement of the paper framework is as follows:in the first chapter,we mainly review the historical development process of the dynamic system,entropy,topological pressure and the research on the current situation in related aspects.In the second chapter,we introduce the classical definitions of measure entropy,measure sequence entropy,topological entropy,topological sequence entropy,topological pressure,measure-theoretical pressure and restate several important theorems.In the third chapter,we use open covering,spanning set and separated set to give the definition of sequence pressure in compact metric space,especially when the real value function is zero,then sequence pressure is topological sequence entropy,also the relation and equivalence between definitions are proved.In the fourth chapter,the classical variational principle is studied.In general,we found that sequence pressure is not less than the sum of measure sequence entropy and function integration in the whole space for any invariant measure.In addition,under some conditions,the relationship between measure entropy and measure sequence entropy is discussed,hence,we discussed the relationship between topological pressure,measure-theoretical pressure and sequence pressure.In the fifth chapter,combined with the discussed content of this paper,the main conclusions are expounded,and the unsolved problems are conjectured.