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Equidistribution of infinite interval substitution schemes, explicit resonances of Anosov toral maps, and the Hausdor dimension of the Rauzy gasket
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Sewell, Benedict Adam (2021) Equidistribution of infinite interval substitution schemes, explicit resonances of Anosov toral maps, and the Hausdor dimension of the Rauzy gasket. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3759900
Abstract
This thesis comprises three chapters: In the first chapter, we consider an infinite analogue of the classical α- Kakutani equidistribution problem, and under mild assumptions, we prove results on uniform distribution and discrepancy, extending results of [34] and others.
In the second chapter, we provide explicit Ruelle resonances for three families of Anosov diffeomorphisms on the two-torus, following and extending results of [88].
In the third chapter, we show that the Hausdorff dimension of the Rauzy gasket is at most 1:7407, improving upon results of [10] and [47].
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Ruelle operators, Hausdorff compactifications, Anosov diffeomorphisms, Torus (Geometry) | ||||
Official Date: | July 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Pollicott, Mark | ||||
Format of File: | |||||
Extent: | iii, 204 leaves : illustrations | ||||
Language: | eng |
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