We define a class of discrete Abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply recurrent. We then study conditions sufficient for showing that Cartesian products of transformations are conservative for a class of invertible infinite measure-preserving transformations and provide examples of these transformations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-1,
author = {Chris Dodd and Phakawa Jeasakul and Anne Jirapattanakul and Daniel M. Kane and Becky Robinson and Noah D. Stein and Cesar E. Silva},
title = {Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {1-22},
zbl = {1190.37006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-1}
}
Chris Dodd; Phakawa Jeasakul; Anne Jirapattanakul; Daniel M. Kane; Becky Robinson; Noah D. Stein; Cesar E. Silva. Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations. Colloquium Mathematicae, Tome 120 (2010) pp. 1-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-1/