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 through a finite chain of such components.
Cite
@article{arxiv.1010.5280,
title = {A Combinatorial classification of postcritically fixed Newton maps},
author = {Kostiantyn Drach and Yauhen Mikulich and Johannes Rückert and Dierk Schleicher},
journal= {arXiv preprint arXiv:1010.5280},
year = {2019}
}
Comments
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