The transformations of Fourth-middle Cantor set and their ergodic measures
WANG Fen1， ZHANG Xiaoyan2
1.School of Mathematics and Economics， Hubei University of Education， Wuhan 430205；2.School of Mathematics and Statistics， Central China Normal University， Wuhan 430079
Abstract：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 is a transformation of T(4，{0,2}) if and only if α＝4n(n∈Z). Then the existence of ergodic measures is considered.
王 芬,张晓艳. Cantor四分集上的变换及其遍历测度[J]. 华中师范大学学报(自然科学版), 2017, 51(2): 140-142.
WANG Fen,ZHANG Xiaoyan. The transformations of Fourth-middle Cantor set and their ergodic measures. journal1, 2017, 51(2): 140-142.
2017, Vol. 51 
