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Speedups of ergodic group extensions

Published online by Cambridge University Press:  01 May 2012

ANDREY BABICHEV ,
ROBERT M. BURTON  and
ADAM FIELDSTEEL
ANDREY BABICHEV
Affiliation:
Wesleyan University, Middletown, CT, USA (email: [email protected])
ROBERT M. BURTON
Affiliation:
Oregon State University, Corvallis, OR, USA (email: [email protected])
ADAM FIELDSTEEL
Affiliation:
Wesleyan University, Middletown, CT, USA (email: [email protected])
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Abstract

We prove that for all ergodic extensions $S_{1}$ of a transformation by a locally compact second countable group $G$, and for all $G$-extensions $ S_{2} $ of an aperiodic transformation, there is a relative speedup of $ S_{1} $ that is relatively isomorphic to $S_{2}$. We apply this result to give necessary and sufficient conditions for two ergodic $n$-point or countable extensions to be related in this way.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 4 , August 2013 , pp. 969 - 982
Copyright
Copyright © 2012 Cambridge University Press 

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