A Classification of Postcritically Finite Newton Maps

Russell Lodge (), Yauhen Mikulich () and Dierk Schleicher ()
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Russell Lodge: Indiana State University, Department of Mathematics and Computer Science
Dierk Schleicher: UMR 7373, Institut de Mathématiques de Marseille, Aix-Marseille Université and CNRS

Chapter Chapter 13 in In the Tradition of Thurston II, 2022, pp 421-448 from Springer

Abstract: Abstract The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some approachable one-parameter families of rational maps; the goal of finding a classification of general rational maps is so far elusive. Newton maps (rational maps that arise when applying Newton’s method to a polynomial) form a most natural family to be studied from the dynamical perspective. Using Thurston’s characterization and rigidity theorem, a complete combinatorial classification of postcritically finite Newton maps is given in terms of a finite connected graph satisfying certain explicit conditions.

Keywords: Newton map; Rational map; Parameter space; Renormalization; Hubbard tree; Combinatorial classification; Extended Newton graph; Thurston’s theorem; Primary 30D05; 37F10; 37F20 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-97560-9_13

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DOI: 10.1007/978-3-030-97560-9_13

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