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Mixing constructions with infinite invariant measure and spectral multiplicities

Published online by Cambridge University Press:  10 May 2010

ALEXANDRE I. DANILENKO  and
VALERY V. RYZHIKOV
ALEXANDRE I. DANILENKO
Affiliation:
Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany (email: alexandre.danilenko@gmail.com)
VALERY V. RYZHIKOV
Affiliation:
Department of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russian Federation (email: vryzh@mail.ru)
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Abstract

We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing power weakly mixing infinite measure preserving transformations, and (iii) construct mixing Poissonian automorphisms with a simple spectrum, etc.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 3 , June 2011 , pp. 853 - 873
Copyright
Copyright © Cambridge University Press 2010

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