Proof of universality for critical circle mappings.
Item
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Title
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Proof of universality for critical circle mappings.
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Identifier
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AAI9304652
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identifier
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9304652
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Creator
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de Faria, Edson.
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Contributor
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Adviser: Dennis P. Sullivan
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Date
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1992
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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In this thesis we employ techniques from quasiconformal mappings and Teichmuller theory to establish a contraction property for the renormalization operator acting on critical circle mappings with a cubic-exponent singularity and rotation number of bounded combinatorial type. As a consequence, we derive the so-called golden mean universality conjecture: the successive scaling ratios of a critical circle mapping as above with rotation number equal to the golden number converge to a universal constant.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
