Rankone flows of transformations with infinite ergodic index
Authors:
Alexandre I. Danilenko and Kyewon K. Park
Journal:
Proc. Amer. Math. Soc. 139 (2011), 201207
MSC (2010):
Primary 37A40; Secondary 37A10, 37A25
Published electronically:
July 6, 2010
MathSciNet review:
2729083
Fulltext PDF
Abstract 
References 
Similar Articles 
Additional Information
Abstract: A rankone infinite measure preserving flow is constructed such that for each , the Cartesian powers of the transformation are all ergodic.
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 A. I. Danilenko and C. E. Silva, Multiple and polynomial recurrence for abelian actions in infinite measure, J. London Math. Soc. 69 (2004), 183200. MR 2025335 (2005a:37008)
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 , Mixing rankone actions of locally compact Abelian groups, Ann. Inst. H. Poincaré, Probab. Statist. 43 (2007), 375398. MR 2329508 (2008j:37005)
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 , Ergodic theory: nonsingular transformations, Encyclopedia of complexity and systems science, Springer, 2009.
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 A. I. Danilenko and V. V. Ryzhikov, Mixing constructions with infinite invariant measure and spectral multiplicities, Ergod. Th. & Dynam. Syst. (to appear), doi:10.1017/S0143385710000052.
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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 442749, Korea
Email:
kkpark@madang.ajou.ac.kr
DOI:
http://dx.doi.org/10.1090/S000299392010104604
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 2007313C00044.
Communicated by:
Bryna Kra
Article copyright:
© Copyright 2010
American Mathematical Society
