On the multiple recurrence properties for disjoint systems

Michihiro Hirayama, Dong Han Kim, Younghwan Son

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider a mutually disjoint family of measure preserving transformations T1, …, Tk on a probability space (Xℬμ). We obtain the multiple recurrence property of T1, …, Tk and this result is utilized to derive multiple recurrence of Poincaré type in metric spaces. We also present the multiple recurrence property of Khintchine type. Further, we study multiple ergodic averages of disjoint systems and we show that T1, …, Tk are uniformly jointly ergodic if each Ti is ergodic.

Original languageEnglish
Pages (from-to)405-431
Number of pages27
JournalIsrael Journal of Mathematics
Volume247
Issue number1
DOIs
StatePublished - Apr 2022

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