IP-sets and polynomial recurrence

Vitaly Bergelson, Hillel Furstenberg, Randall McCutcheon

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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.

Original languageEnglish
Pages (from-to)963-974
Number of pages12
JournalErgodic Theory and Dynamical Systems
Issue number5
StatePublished - Oct 1996
Externally publishedYes


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