Multiple common expansions in non-integer bases

Vilmos Komornik, Marco Pedicini, A. Pethő

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate the existence of simultaneous representations of real numbers x in bases 1 < q1 < ⋯ < qr, r ≥ 2, with a finite digit set A ⊃ ℝ. We prove that if A contains both positive and negative digits, then each real number has infinitely many common expansions. In general the bases depend on x. If A contains the digits -1,0,1, then there exist two non-empty open intervals I, J such that for any fixed qi ϵ I each x ϵ J has common expansions for some bases q1 < ⋯ qr.

Original languageEnglish
Pages (from-to)51-60
Number of pages10
JournalActa Scientiarum Mathematicarum
Volume83
Issue number1-2
DOIs
Publication statusPublished - Jan 1 2017

    Fingerprint

Keywords

  • Interval filling sequences
  • Simultaneous Rényi expansions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this