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Partitions with independent iterates along IP-Sets

Published online by Cambridge University Press:  02 April 2001

ANDRES DEL JUNCO ,
KARIN REINHOLD  and
BENJAMIN WEISS
ANDRES DEL JUNCO
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1 (e-mail: [email protected])
KARIN REINHOLD
Affiliation:
Department of Mathematics,SUNY Albany, Albany NY 12222, USA (e-mail: [email protected])
BENJAMIN WEISS
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel (e-mail: [email protected])
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Abstract

We prove a collection of results inspired by Krengel's theorem on the existence of partitions with infinitely many independent iterates in any weakly mixing measure-preserving dynamical system. Our approach avoids Krengel's use of two-fold mixing thereby obtaining stronger results, including characterizations of mild and strong mixing, as well as weak mixing. We also obtain results for non-weakly mixing systems and for more general group actions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 2 , April 1999 , pp. 447 - 473
Copyright
1999 Cambridge University Press

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