The Shrinking Target Problem for Matrix Transformations of Tori: revisiting the standard problem

Bing Li, Lingmin Liao, Sanju Velani +2

Let $T$ be a $d\times d$ matrix with real coefficients. Then $T$ determines a self-map of the $d$-dimensional torus ${\mathbb{T}}^d={\mathbb{R}}^d/{\mathbb{Z}}^d$. Let $ \{E_n \}_{n \in \m…