Denseness of intermediate β-shifts of finite-type

Bing Li; Tuomas Sahlsten; Tony Samuel; Wolfgang Steiner

doi:10.1090/proc/14279

Denseness of intermediate β-shifts of finite-type

Bing Li, Tuomas Sahlsten, Tony Samuel, Wolfgang Steiner

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

135 Downloads (Pure)

Abstract

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) ∈ R^{2 :} β ∈ (1, 2) and 0 ≤ α ≤ 2 − β}. This generalises the classical result of Parry from 1960 for greedy β-shifts.

Original language	English
Pages (from-to)	2045–2055
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	5
Early online date	6 Feb 2019
DOIs	https://doi.org/10.1090/proc/14279
Publication status	Published - 2019

Keywords

Interval map
Subshifts of finite type
Kneading theory
β-transformations

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Tony_Samuel_et_al_Denseness_of_intermediate_β-shifts_Proceedings_of_the_American_Mathematical_Society_2018
First published in Proceedings of the American Mathematical Society in Vol. 147, No. 5, 2019, published by the American Mathematical Society. © Copyright 2019 American Mathematical Society
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AB - 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.

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KW - β-transformations

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Denseness of intermediate β-shifts of finite-type

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Keywords

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