Self-affine sets with positive Lebesgue measure

Karma Dajani, Kan Jiang, Thomas Michael William Kempton

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
3 Downloads (Pure)

Abstract

Using techniques introduced by C. Gunturk, we prove that the attractors of a
family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous
β-expansion’ of different numbers in different bases.
Original languageEnglish
Pages (from-to)774-784
JournalIndagationes Mathematicae
Volume25
Issue number4
Early online date9 May 2014
DOIs
Publication statusPublished - 27 Jun 2014

Keywords

  • Overlapping self-affine sets
  • Iterated function systems
  • Beta expansions

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