Sets of transfer times with small densities

Journal article, 2021

In this paper we introduce and discuss various notions of doubling for measurepreserving actions of a countable abelian group G. Our main result characterizes 2-doubling actions, and can be viewed as an ergodic-theoretical extension of some classical density theorems for sumsets by Kneser. All of our results are completely sharp and they are new already in the case when G = (Z; +).