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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

   
 

 

Ergodic homoclinic groups, Sidon constructions and Poisson suspensions


Author: V. V. Ryzhikov
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 75 (2014), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2014, 77-85
MSC (2010): Primary 28D05
Published electronically: November 5, 2014
MathSciNet review: 3308601
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Abstract: We give some new examples of mixing transformations on a space with infinite measure: the so-called Sidon constructions of rank 1. We obtain rapid decay of correlations for a class of infinite transformations; this was recently discovered by Prikhod'ko for dynamical systems with simple spectrum acting on a probability space. We obtain an affirmative answer to Gordin's question about the existence of transformations with zero entropy and an ergodic homoclinic flow. We consider modifications of Sidon constructions inducing Poisson suspensions with simple singular spectrum and a homoclinic Bernoulli flow. We give a new proof of Roy's theorem on multiple mixing of Poisson suspensions.


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Additional Information

V. V. Ryzhikov
Affiliation: Moscow State University
Email: vryzh@mail.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00227-2
Keywords: Ergodic actions, rank-one construction, Sidon set, multiple mixing, Poisson suspension, homoclinic transformations, singular spectrum
Published electronically: November 5, 2014
Article copyright: © Copyright 2014 V. V. Ryzhikov