Cantor四分集上的变换及其遍历测度

摘要

该文给出了Tα(x)=αx(mod 1)(α∈R+)是Cantor四分集T(4,{0,2})上的变换的充要条件:Tα为T(4,{0,2})上的变换当且仅当α=4n(n∈Z).并且研究了Tα的遍历测度的存在性.%In this paper,the sufficient and necessary condition is provided for Tα(x) =αx (mod 1)(α ∈ R+) to be transformations of Fourth-Middle Cantor set T(4,{0,2}):Tα isatransformationofT(4,{0,2})ifandonlyifα=4n(n ∈ Z).Then the existence of ergodic measures is considered.