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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rank-one flows of transformations with infinite ergodic index


Authors: Alexandre I. Danilenko and Kyewon K. Park
Journal: Proc. Amer. Math. Soc. 139 (2011), 201-207
MSC (2010): Primary 37A40; Secondary 37A10, 37A25
Published electronically: July 6, 2010
MathSciNet review: 2729083
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Abstract: A rank-one infinite measure preserving flow $ T=(T_{t})_{t\in \mathbb{R}}$ is constructed such that for each $ t\ne 0$, the Cartesian powers of the transformation $ T_{t}$ are all ergodic.


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Additional Information

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

Kyewon K. Park
Affiliation: Department of Mathematics, College of Natural Science, Ajou University, Suwon 442-749, Korea
Email: kkpark@madang.ajou.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10460-4
PII: S 0002-9939(2010)10460-4
Keywords: Infinite ergodic index, $(C, F)$-construction.
Received by editor(s): October 14, 2009
Received by editor(s) in revised form: February 23, 2010
Published electronically: July 6, 2010
Additional Notes: The first author thanks Ajou University and KIAS for supporting in part his visit to South Korea.
The second author is supported in part by KRF 2007-313-C00044.
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society