On the classification of plane graphs representing structurally stable rational Newton flows

We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles b...

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Bibliographic Details
Published inJournal of combinatorial theory. Series B Vol. 51; no. 2; pp. 256 - 270
Main Authors Jongen, H.Th, Jonker, P, Twilt, F
Format Journal Article
LanguageEnglish
Published Duluth, MN Elsevier Inc 01.03.1991
Academic Press
Subjects
Combinatorics. Ordered structures
Exact sciences and technology
Mathematics
Sciences and techniques of general use
Iterative method
Newtonian flow
Dynamical system
Classification
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Summary:We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles between edges at the same vertex. We derive necessary and sufficient conditions—of purely combinatorial nature—for an arbitrary plane graph in order to be topologically equivalent with a Newton graph. Finally, we analyse the structure of Newton graphs and prove the existence of a polynomial algorithm to recognize such graphs.
ISSN:0095-8956
1096-0902
DOI:10.1016/0095-8956(91)90041-H