Times two, three, five orbits on ${\mathbb{T}}^2$

Abstract

In this paper, we study orbit closures under diagonal torus actions. We show that if $(x,y)\in {\mathbb{T}}^2$ is not contained in any rational lines, then its orbit under the $\times 2,\times 3,\times 5$ actions is dense in ${\mathbb{T}}^2.$

14 pages, 1 figure; Version accepted in Adv. Math