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Induced random β-transformation

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Baker, Simon and Dajani, Karma (2017) Induced random β-transformation. Acta Arithmetica, 178 . pp. 1-14. doi:10.4064/aa8306-8-2016

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Official URL: https://doi.org/10.4064/aa8306-8-2016

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Abstract

In this article we study the first return map defined on the switch region induced by the greedy and lazy maps. In particular we study the allowable sequences of return times, and when the first return map is a generalised L¨uroth series transformation. We show that there
exists a countable collection of disjoint intervals (In)∞n=1, such that all sequences of return times are permissible if and only if β ∈ In for some n. Moreover, we show that there exists a set M ⊆ (1, 2) of Hausdorff dimension 1 and Lebesgue measure zero, for which the first return map is a generalised L¨uroth series transformation if and only if β ∈ M.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Acta Arithmetica
Publisher: Polska Akademia Nauk: Instytut Matematyczny
ISSN: 0065-1036
Official Date: 17 February 2017
Dates:
DateEvent
17 February 2017Available
17 February 2017Accepted
Volume: 178
Page Range: pp. 1-14
DOI: 10.4064/aa8306-8-2016
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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