A two dimensional analog of the three gap theorem

Yury Kochetkov, Alexandr Osipov

For a two dimensional vector $\bar{v}=(\alpha ,\beta )$, where $\alpha >0,\beta >0$ are irrational numbers independent over $\mathbb{Q}$, we consider the set $D_n=\{(iα\,{\rm mod}\,1,iβ\,{\rm mod}\,1),i…