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Finite ergodic index and asymmetry for infinite measure preserving actions


Author: Alexandre I. Danilenko
Journal: Proc. Amer. Math. Soc. 144 (2016), 2521-2532
MSC (2010): Primary 37A40
DOI: https://doi.org/10.1090/proc/12906
Published electronically: October 5, 2015
MathSciNet review: 3477068
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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$.


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Additional Information

Alexandre I. Danilenko
Affiliation: Institute for Low Temperature Physics & Engineering of National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61164, Ukraine
Email: alexandre.danilenko@gmail.com

DOI: https://doi.org/10.1090/proc/12906
Received by editor(s): December 13, 2014
Received by editor(s) in revised form: June 19, 2015, and July 11, 2015
Published electronically: October 5, 2015
Communicated by: Nimish Shah
Article copyright: © Copyright 2015 American Mathematical Society