拓扑强链遍历映射

Topological Strongly Chain Ergodicity Maps

通过引进强链遍历性的概念,证明了f拓扑遍历蕴含f强链遍历.对任意正整数k,fk强链遍历蕴含f强链遍历;若f满足Lipschitz条件,k是任意正整数,f强链遍历当且仅当fk强链遍历.集值映射f:κ(X)→κ(X)强链遍历蕴含f:X→X强链遍历.证明了紧致系统(X,f)的强链遍历性与其提升系统(X槇,f槇)的强链遍历性是等价的.

The paper proves that f topologically ergodic implies f strongly chain ergodie by introdu- cing the definition of strongly chain ergodicity. It shows fk strongly chain ergodic implies f strongly chain ergodic for every positive integerk; If f satisfies Lipschitz condition, fk strongly chain ergodic if and only if f strongly chain ergodic for every positive integerk. The paper investigates set-valued map f：κ（X）→κ（X） strongly chain ergodic implies f： X→X strongly chain ergodic, and it also proves that strongly chain ergodic property of （X,f） and strongly chain ergodic property for its lift system （~X,~f） is equivalent.