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Minimizing entropy for translation surfaces
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Colognese, Paul and Pollicott, Mark (2022) Minimizing entropy for translation surfaces. Conformal Geometry and Dynamics, 26 (6). pp. 97-110. doi:10.1090/ecgd/374 ISSN 1088-4173.
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Official URL: https://doi.org/10.1090/ecgd/374
Abstract
In this note we consider the entropy by Dankwart [On the large-scale geometry of flat surfaces, 2014, PhD thesis. https://bib.math.uni-bonn.de/downloads/bms/BMS-401.pdf] of unit area translation surfaces in the orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices. We also provide a method for approximating the entropy of surfaces in the orbits.
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): | Topological entropy, Topological dynamics, Differentiable dynamical systems, Singularities (Mathematics) | |||||||||
Journal or Publication Title: | Conformal Geometry and Dynamics | |||||||||
Publisher: | American Mathematical Society | |||||||||
ISSN: | 1088-4173 | |||||||||
Official Date: | 2022 | |||||||||
Dates: |
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Volume: | 26 | |||||||||
Number: | 6 | |||||||||
Page Range: | pp. 97-110 | |||||||||
DOI: | 10.1090/ecgd/374 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Re-use Statement: | First published in Geometry and Dynamics, 26 (6). pp. 97-110 (2022) Published by the American Mathematical Society. | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 11 November 2022 | |||||||||
Date of first compliant Open Access: | 11 November 2022 | |||||||||
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