Dimension bound for badly approximable grids

Seonhee Lim, Nicolas de Saxcé, Uri Shapira

We show that for almost any vector $v$ in ${\mathbb{R}}^n$, for any $\epsilon >0$ there exists $\delta >0$ such that the dimension of the set of vectors $w$ satisfying $\liminf_{k\to\infty} k^{1/n…