Schmidt's game, fractals, and orbits of toral endomorphisms

Ryan Broderick, Lior Fishman, Dmitry Kleinbock

Given an integer nonsingular $n\times n$ matrix $M$ and a point $y\in {\mathbb{R}}^n/{\mathbb{Z}}^n$, consider the set $\tilde{E}(M,y)$ of vectors $x\in {\mathbb{R}}^n$ such that $y$ is…