Khintchine-type double recurrence in abelian groups
Khintchine-type double recurrence in abelian groups
Abstract We prove a Khintchine-type recurrence theorem for pairs of endomorphisms of a countable discrete abelian group. As a special case of the main result, if $\Gamma $ is a countable discrete abelian group, $\varphi , \psi \in \mathrm {End}(\Gamma )$ , and $\psi - \varphi $ is an injective …