Uniform Diophantine approximation on the plane for $\beta$-dynamical systems

Xiaohui Fu, Junjie Shi, Chen Tian

In this paper, we investigate the two-dimensional uniform Diophantine approximation in $\beta$-dynamical systems. Let ${\beta }_i>1(i=1,2)$ be real numbers, and let $T_{{\beta }_i}$ denote the $β_…