Denseness of intermediate β-shifts of finite-type

Bing Li, Tuomas Sahlsten, Tony Samuel, Wolfgang Steiner

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
113 Downloads (Pure)


We determine the structure of the set of intermediate β-shifts of finite-type. Specifically, we show that this set is dense in the parameter space Δ := {(β,α) ∈ R2 : β ∈ (1, 2) and 0 ≤ α ≤ 2 − β}. This generalises the classical result of Parry from 1960 for greedy β-shifts.
Original languageEnglish
Pages (from-to)2045–2055
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number5
Early online date6 Feb 2019
Publication statusPublished - 2019


  • Interval map
  • Subshifts of finite type
  • Kneading theory
  • β-transformations


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