Variations on topological recurrence

Bernard Host, Bryna Kra*, Alejandro Maass

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate finite versions of recurrence, and describe connections to combinatorial problems. In particular, we show that sets of Bohr recurrence (meaning sets of recurrence for rotations) suffice for recurrence in nilsystems. Additionally, we prove an extension of this property for multiple recurrence in affine systems.

Original languageEnglish (US)
Pages (from-to)57-89
Number of pages33
JournalMonatshefte fur Mathematik
Volume179
Issue number1
DOIs
StatePublished - Jan 1 2016

Keywords

  • Multiple recurrence
  • Nilsystem
  • Recurrence
  • Topological dynamics

ASJC Scopus subject areas

  • Mathematics(all)

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