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Rigorous dimension estimates for Cantor sets arising in Zaremba theory
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Jenkinson, Oliver and Pollicott, Mark (2020) Rigorous dimension estimates for Cantor sets arising in Zaremba theory. In: Moree, Pieter and Pohl, Anke and Snoha, L’ubomír and Ward, Tom, (eds.) Dynamics : topology and numbers. Contemporary Mathematics, 744 . Providence, Rhode Island: American Mathematical Society, pp. 83-107. ISBN 9781470451004
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WRAP-rigorous-dimension-estimates-Cantor-sets-arising-theory-Pollicott-2019.pdf - Accepted Version - Requires a PDF viewer. Download (948Kb) | Preview |
Official URL: https://doi.org/10.1090/conm/744
Abstract
We address the question of the accuracy of bounds used in the study of Zaremba’s conjecture. Specifically, we establish rigorous estimates on the Hausdorff dimension of certain Cantor sets which arise in the analysis of Zaremba’s conjecture in [5, 18, 19, 23].
| Item Type: | Book Item | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Cantor sets , Hausdorff measures , Euclidean algorithm | ||||||
| Series Name: | Contemporary Mathematics | ||||||
| Journal or Publication Title: | Contemporary Mathematics | ||||||
| Publisher: | American Mathematical Society | ||||||
| Place of Publication: | Providence, Rhode Island | ||||||
| ISBN: | 9781470451004 | ||||||
| ISSN: | 0271-4132 | ||||||
| Book Title: | Dynamics : topology and numbers | ||||||
| Editor: | Moree, Pieter and Pohl, Anke and Snoha, L’ubomír and Ward, Tom | ||||||
| Official Date: | 2020 | ||||||
| Dates: |
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| Volume: | 744 | ||||||
| Page Range: | pp. 83-107 | ||||||
| Article Number: | 0271-4132 | ||||||
| DOI: | 10.1090/conm/744 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | “First published in Dynamics : topology and numbers in Volume 744 2020, published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 21 May 2019 | ||||||
| Date of first compliant Open Access: | 21 May 2019 | ||||||
| Conference Paper Type: | Paper | ||||||
| Title of Event: | Conference on dynamics : topology and numbers | ||||||
| Type of Event: | Conference | ||||||
| Location of Event: | Bonn, Germany | ||||||
| Date(s) of Event: | 2-6 Jul 2018 | ||||||
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