Finite ergodic index and asymmetry for infinite measure preserving actions

Abstract

Given $k>0$ and an Abelian countable discrete group $G$ with elements of infinite order, we construct $(i)$ rigid funny rank-one infinite measure preserving (i.m.p.) $G$-actions of ergodic index $k$, $(ii)$ 0-type funny rank-one i.m.p. $G$-actions of ergodic index $k$, $(iii)$ funny rank-one i.m.p. $G$-actions $T$ of ergodic index 2 such that the product $T\times T^{-1}$ is not ergodic. It is shown that $T\times T^{-1}$ is conservative for each funny rank-one $G$-action $T$.

arXiv commentLemma 1.1(ii) is corrected. This implied little changes in the proof of Claim 1 in Theorems 0.1 and 0.3

References in corpus (1)

• On Infinite Transformations with Maximal Control of Ergodic Two-fold Product Powers