Topological Entropy Pairs And Topological Pressure For An Iterated Function System

In this paper,we introduce a new topological entropy in an iterated function system,this topological entropy is different from the concept of topological entropy introduced by the authors,it is proved that the topological entropy has very important properties,that is subadditivity.Starting from the concept of topological entropy,the concept of topological entropy pairs is introduced and some properties of it are discussed.An interesting result is obtained.When the value of topological entropy is greater than zero,then the set of entropy pairs is nonempty.Meanwhile,we extend this new topological entropy to topological pressure in an iterated function system,several equivalent definitions of the topological pressure are obtained.The topological pressure can be defined by using spanning subsets,separating subsets and open covers.It is showed that the topological pressure is smaller than that defined by other authors.After that,we also study the properties of the topological pressure.We find out the properties of the topological pressure which are more similar to the properties of classical topological pressure than other authors.Finally,the topological pressure is associated with measure-theoretic entropy and measure integral,a partial variational principle is obtained.That is,for an iterated function system(X,F),we prove h?(F)+(?)???P(F,?)for all invariant measure ? and ??C(X,R),where h?(F)is the measure-theoretic entropy of(X,F)for ? and P(F,?)is the topological pressure of ?.