标题： $(α,β)$移位的规格 Hausdorff 维数 显示英文标题

标题： Hausdorff dimension of specification for the $(α,β)$-shifts

摘要： 规范是动力系统中由Bowen引入的重要概念。 Schmeling证明了使得相应$\beta$-移位具有规范性的$\beta>1$的集合的豪斯多夫维数为$1$。 Hu等人证明了使得相应$(-\beta)$-移位具有规范性的$\beta>1$的集合的豪斯多夫维数为$1$。 我们证明了满足对应$(\alpha,\beta)$-移位具有规范性的$(\alpha,\beta)\in[0,1)\times(1,\infty)$集合的豪斯多夫维数为$2$。一个新的困难是同时控制两个决定环境移位空间的关键符号序列。我们通过在参数空间中取两个稠密康托尔集的交集来实现这一点。 显示英文摘要

摘要： Specification is an important concept in dynamical systems introduced by Bowen. Schmeling proved that the set of $\beta>1$ such that the corresponding $\beta$-shift has specification is of Hausdorff dimension $1$. Hu et al. proved that the set of $\beta>1$ such that the corresponding $(-\beta)$-shift has specification is of Hausdorff dimension $1$. We show that the set of $(\alpha,\beta)\in[0,1)\times(1,\infty)$ such that the corresponding $(\alpha,\beta)$-shift has specification is of Hausdorff dimension $2$. A new difficulty is a simultaneous control of two critical symbol sequences that determine the ambient shift space. We achieve this by taking intersections of two thick Cantor sets in parameter space.