A classification of postcritically finite Newton maps
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.
Cite
@article{arxiv.1510.02771,
title = {A classification of postcritically finite Newton maps},
author = {Russell Lodge and Yauhen Mikulich and Dierk Schleicher},
journal= {arXiv preprint arXiv:1510.02771},
year = {2022}
}
Comments
This paper will appear in the book: In the Tradition of Thurston, Vol. II, ed. K. Ohshika and A. Papadopoulos, Springer, 2022