A polynomial-exponential variation of Furstenberg's theorem

M. Abramoff, D. Berend

Research output: Contribution to journalArticlepeer-review

Abstract

Furstenberg's theorem asserts that the double sequence is dense modulo one for every irrational. The same holds with and replaced by any two multiplicatively independent integers. Here we obtain the same result for the sequences for any non-negative integer and irrational, and for the sequence, where is any polynomial with at least one irrational coefficient. Similarly to Furstenberg's theorem, both results are obtained by considering appropriate dynamical systems.

Original languageEnglish
Pages (from-to)1729-1737
Number of pages9
JournalErgodic Theory and Dynamical Systems
Volume40
Issue number7
DOIs
StatePublished - 1 Jul 2020

Keywords

  • Density modulo 1
  • Furstenberg's diophantine theorem
  • topological dynamics

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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