A classification of postcritically finite Newton maps

  • One of the most important open problems in rational dynamics is understanding the structure of the space of rational functions. Newton maps of polynomials form an interesting subset of the space of rational maps that is more accessible for studying than the full space of rational maps. For every postcritically finite Newton map N_p of a polynomial p we construct a finite connected graph that contains the postcritical set of N_p. We show that such graphs characterize Newton maps uniquely up to Moebius conjugation. Conversely, we show that every graph with an associated map that satisfies particular conditions is realized by a unique postcritically finite Newton map. We show that there is a mapping from the set of postcritically finite Newton maps up to Moebius equivalence to the set of abstract extended Newton graphs with the corresponding equivalence relation on them. We show that this mapping is one to one, giving thereby a combinatorial classification of postcritically finite Newton maps in terms of finite connected graphs.

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Meta data
Publishing Institution:IRC-Library, Information Resource Center der Jacobs University Bremen
Granting Institution:Jacobs Univ.
Author:Yauhen Mikulich
Referee:Dierk Schleicher, Daniel Meyer, Vladlen Timorin
Advisor:Dierk Schleicher
Persistent Identifier (URN):urn:nbn:de:101:1-2013052812179
Document Type:PhD Thesis
Language:English
Date of Successful Oral Defense:2011/09/26
Date of First Publication:2011/12/13
PhD Degree:Mathematics
Library of Congress Classification:Q Science / QA Mathematics (incl. computer science)
School:SES School of Engineering and Science
Call No:Thesis 2011/43

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