Plane trees, Shabat-Zapponi polynomials and Julia sets
Dynamical Systems
2016-09-01 v1
Abstract
A tree, embedded into plane, is a dessin d'enfant and its Belyi function is a polynomial --- Shabat polynomial. The Zapponi form of this polynomial is unique, so we can correspond to an embedded tree the Julia set of its Shabat-Zapponi polynomial. In this purely experimental work we study relations between the form of a tree and properties (form, connectedness, Hausdorff dimension) of its Julia set.
Keywords
Cite
@article{arxiv.1608.08866,
title = {Plane trees, Shabat-Zapponi polynomials and Julia sets},
author = {Yury Kochetkov},
journal= {arXiv preprint arXiv:1608.08866},
year = {2016}
}
Comments
12 pages, 6 figures