Topological model of simple Siegel disk type.

Title: Topological model of simple Siegel disk type.
Identifier: AAI3063900
identifier: 3063900
Creator: Zhang, Gaofei.
Contributor: Adviser: Yunping Jiang
Date: 2002
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Around 1982, Thurston developed a rational realization and rigidity theory for the critically finite branched covering maps. Since then, people have been trying to generalize this theory to critically infinite maps. In this work, we established a Thurston type theory for topological polynomials of simple Siegel disk type. We proved that a topological polynomial of simple Siegel disk type is combinatorially equivalent to a canonical polynomial with a Siegel disk if and only if it has no Thurston obstruction. We then present a way to prove that the Julia set of the canonical polynomial has Lebesgue measure zero, which implies that up to a conformal conjugation, the canonical polynomial is the unique polynomial to realize the topological model such that the boundary of the Siegel disk is a quasi-circle.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.