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Dyadic approximation in the middle-third Cantor set
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Allen, Demi, Chow, Sam and Yu, Han (2022) Dyadic approximation in the middle-third Cantor set. Selecta Mathematica, New Series, 29 . 11. doi:10.1007/s00029-022-00814-x ISSN 1022-1824.
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Official URL: https://doi.org/10.1007/s00029-022-00814-x
Abstract
In this paper, we study the metric theory of dyadic approximation in the middle-third Cantor set. This theory complements earlier work of Levesley, Salp, and Velani (2007), who investigated the problem of approximation in the Cantor set by triadic rationals. We find that the behaviour when we consider dyadic approximation in the Cantor set is substantially different to considering triadic approximation in the Cantor set. In some sense, this difference in behaviour is a manifestation of Furstenberg's times 2 times 3 phenomenon from dynamical systems, which asserts that the base 2 and base 3 expansions of a number are not both structured.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Diophantine approximation, Algebra, Number theory, Cantor sets, Hausdorff measures | ||||||||||||
Journal or Publication Title: | Selecta Mathematica, New Series | ||||||||||||
Publisher: | Birkhauser Verlag AG | ||||||||||||
ISSN: | 1022-1824 | ||||||||||||
Official Date: | 29 November 2022 | ||||||||||||
Dates: |
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Volume: | 29 | ||||||||||||
Article Number: | 11 | ||||||||||||
DOI: | 10.1007/s00029-022-00814-x | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 30 September 2022 | ||||||||||||
Date of first compliant Open Access: | 14 December 2022 | ||||||||||||
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