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A combinatorial classification of postcritically fixed Newton maps

Published online by Cambridge University Press:  13 March 2018

KOSTIANTYN DRACH ,
YAUHEN MIKULICH ,
JOHANNES RÜCKERT  and
DIERK SCHLEICHER
KOSTIANTYN DRACH
Affiliation:
Jacobs University Bremen, Research I, Campus Ring 1, 28759 Bremen, Germany email k.drach@jacobs-university.de, y.mikulich@gmail.com, jrueckert@jacobs-alumni.de, dierk@jacobs-university.de
YAUHEN MIKULICH
Affiliation:
Jacobs University Bremen, Research I, Campus Ring 1, 28759 Bremen, Germany email k.drach@jacobs-university.de, y.mikulich@gmail.com, jrueckert@jacobs-alumni.de, dierk@jacobs-university.de
JOHANNES RÜCKERT
Affiliation:
Jacobs University Bremen, Research I, Campus Ring 1, 28759 Bremen, Germany email k.drach@jacobs-university.de, y.mikulich@gmail.com, jrueckert@jacobs-alumni.de, dierk@jacobs-university.de
DIERK SCHLEICHER
Affiliation:
Jacobs University Bremen, Research I, Campus Ring 1, 28759 Bremen, Germany email k.drach@jacobs-university.de, y.mikulich@gmail.com, jrueckert@jacobs-alumni.de, dierk@jacobs-university.de
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Abstract

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental ingredient is the proof that for every Newton map (postcritically finite or not) every connected component of the basin of an attracting fixed point can be connected to $\infty$ through a finite chain of such components.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 11 , November 2019 , pp. 2983 - 3014
Copyright
© Cambridge University Press, 2018 

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