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IP-sets and polynomial recurrence

Published online by Cambridge University Press:  14 October 2010

Vitaly Bergelson ,
Hillel Furstenberg  and
Randall McCutcheon
Vitaly Bergelson
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio, 43210, USA
Hillel Furstenberg
Affiliation:
Landau Center for Analysis, Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Randall McCutcheon
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio, 43210, USA
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Abstract

We combine recurrence properties of polynomials and IP-sets and show that polynomials evaluated along IP-sequences also give rise to Poincaré sets for measure-preserving systems, that is, sets of integers along which the analogue of the Poincaré recurrence theorem holds. This is done by applying to measure-preserving transformations a limit theorem for products of appropriate powers of a commuting family of unitary operators.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 5 , October 1996 , pp. 963 - 974
Copyright
Copyright © Cambridge University Press 1996

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References

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