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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
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 | ||||||
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| 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: |
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| 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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