Spectral rigidity of group actions: Applications to the case gr
Author:
Oleg N. Ageev
Journal:
Proc. Amer. Math. Soc. 134 (2006), 13311338
MSC (2000):
Primary 37A05, 37A15, 37A25, 37A30, 37A35, 28D05, 28D15; Secondary 47A05, 47A35, 47D03
Published electronically:
October 6, 2005
MathSciNet review:
2199176
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We apply a technique to study the notion of spectral rigidity of group actions to a group gr. As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a wellknown question.
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 G. Goodson, A survey of recent results in the spectral theory of ergodic dynamical systems, J. Dynam. Control Systems 5 (1999), 173226. MR 1693318 (2000f:28021)
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 G. Goodson, Ergodic dynamical systems conjugate to their composition squares, Acta Math. Univ. Comenian. (N.S.) 71 (2002), 201210. MR 1980380 (2004c:37008)
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 G. Goodson, Spectral properties of ergodic dynamical systems conjugate to their composition squares, preprint.
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 A. del Junco, Transformations with discrete spectrum are stacking transformations, Canad. J. Math. 24 (1976), 836839. MR 0414822 (54:2914)
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 A. del Junco, Disjointness of measurepreserving transformations, selfjoinings and category, Prog. Math. K (1981), 8189. MR 0633762 (82m:28035)
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 D. Ornstein, B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Analyse Math. 48 (1987), 1141. MR 0910005 (88j:28014)
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Additional Information
Oleg N. Ageev
Affiliation:
Department of Mathematics, Moscow State Technical University, 2nd Baumanscaya St. 5, 105005 Moscow, Russia
Address at time of publication:
Max Planck Institute of Mathematics, P.O. Box 7280, D53072 Bonn, Germany
Email:
ageev@mx.bmstu.ru, ageev@mpimbonn.mpg.de
DOI:
http://dx.doi.org/10.1090/S0002993905083802
PII:
S 00029939(05)083802
Keywords:
Group actions,
ergodic theory,
conjugations to its squares
Received by editor(s):
November 20, 2004
Published electronically:
October 6, 2005
Additional Notes:
The author was supported in part by the Max Planck Institute of Mathematics, Bonn, and the Programme of Support of Leading Scientific Schools of the RF (grant no. NSh457.2003.1)
Communicated by:
Michael Handel
Article copyright:
© Copyright 2005 American Mathematical Society
