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Complex bounds for interval maps
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Trejo Abad, Sofía (2013) Complex bounds for interval maps. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2730521~S1
Abstract
In this thesis we give a proof of complex bounds for real analytic interval maps, for all possible combinatorics. We begin by constructing a sequence of intervals, known as the enhanced nest, that covers both non-renormalizable and infinitely renormalizable maps. This is a generalisation of the nest introduced in [KSvS1]. In Chapter 3, we prove the combinatorial and geometric properties of the enhanced nest, known as real bounds. The results from this chapter extend the ones in [KSvS1] to maps with odd critical points. In Chapter 4, we make use of Poincar´e disks based on intervals from the enhanced nest to construct quasi box-mappings associated to (real) first return maps. Key in this part of the proof are the pullbacks along monotone branches, that are controlled with the aid of fundamental domains, and the pullbacks between two consecutive levels from the enhanced nest of different combinatorial type, one non-terminating and one terminating. We use similar techniques to the ones developed in [LevS2] to obtain complex box-mappings from the quasi box-mappings that we constructed. Finally, we follow the arguments in [KSvS1] to prove complex bounds for the complex box-mappings we constructed.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Mappings (Mathematics) | ||||
Official Date: | September 2013 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Strien, Sebastian van, 1956- | ||||
Sponsors: | Consejo Nacional de Ciencia y Tecnología (Mexico) (212227) ; Mexico. Secretaría de Educación Pública ; University of Warwick. Mathematics Institute | ||||
Extent: | vi, 131 leaves : illustrations | ||||
Language: | eng |
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