Modified shrinking target problem for Matrix Transformations of Tori

Na Yuan, ShuaiLing Wang

We calculate the Hausdorff dimension of the fractal set \begin{equation*} \Big\{\mathtt{x}\in \mathbb{T}^d: \prod_{1\leq i\leq d}|T_{β_i}^n(x_i)-x_i| < ψ(n) \text{ for infinitely m…