On rationally ergodic and rationally weakly mixing rank-one transformations

Abstract

AbstractWe study the notions of weak rational ergodicity and rational weak mixing as defined by J. Aaronson [Rational ergodicity and a metric invariant for Markov shifts.Israel J. Math. 27(2) (1977), 93–123; Rational weak mixing in infinite measure spaces.Ergod. Th. & Dynam. Sys.2012, to appear.http://arxiv.org/abs/1105.3541]. We prove that various families of infinite measure-preserving rank-one transformations possess or do not posses these properties, and consider their relation to other notions of mixing in infinite measure.