Winning property of distal set for beta-transformations
Winning property of distal set for beta-transformations
复制标题
β 变换远端组的获胜特性
DOI：
10.1080/14689367.2020.1844154
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Wang Shuailing
中科院分区：
文献类型：
--
作者：
Yang Qianqian;Wang Shuailing
For any, letbe theβ-transformation dynamical system. For any, define the distal set of a given pointyas Dβ(y)={x∈[0,1):lim infn→∞|Tβn(x)−Tβn(y)|>0}Yang, Li, et al. proved that the Hausdorff dimension of the distal set of any point is one for any β>1. In this paper, we study the winning property of the distal set of a given pointy. We prove that the distal set of a given pointyisα-winning for anyand, whereis a constant. By the definition of winning set, it's obvious that the distal set of a given point y is a dense set.
