β-变换远集的获胜性质

Pub Date : 2020-11-29 DOI:10.1080/14689367.2020.1844154

Qianqian Yang, Shuailing Wang

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引用次数: 0

摘要

对于任意，设为β-变换动力系统。对于任意，定义给定点y的远端集为Yang, Li, et al.[15]证明了任意点的远端集的Hausdorff维数对于任意β>1为1。本文研究了给定点y的远端集合的致胜性质，证明了给定点y的远端集合对任意和都是α-致胜的，其中为常数。根据获胜集的定义，可以明显地看出，给定点y的远端集是一个稠密集。

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Winning property of distal set for β-transformations

For any , let be the β-transformation dynamical system. For any , define the distal set of a given point y as Yang, Li, et al. [15] 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 point y. We prove that the distal set of a given point y is α-winning for any and , where is a constant. By the definition of winning set, it's obvious that the distal set of a given point y is a dense set.

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