A Combinatorial classification of postcritically fixed Newton maps

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.

37 pages, 5 figures, published in Ergodic Theory and Dynamical Systems (2018). This is the final author file before publication. Text overlap with earlier arxiv file observed by arxiv system relates to an earlier version that was erroneously uploaded separately. arXiv admin note: text overlap with arXiv:math/0701176

References in corpus (2)

• Newton's method in practice: finding all roots of polynomials of degree one million efficiently
• On Newton's Method for Entire Functions

Cited by in corpus (2)

• Eliminating Thurston obstructions and controlling dynamics on curves
• Dynamics of projectable functions: Towards an atlas of wandering domains for a family of Newton maps