Author:
Bergelson Vitaly,Furstenberg Hillel,McCutcheon Randall
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
36 articles.
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