Equilateral Triangulations and The Postcritical Dynamics of Meromorphic Functions
Dynamical Systems
2022-11-01 v2 Complex Variables
Abstract
We show that any dynamics on any planar set discrete in some domain can be realized by the postcritical dynamics of a function holomorphic in , up to a small perturbation. A key step in the proof, and a result of independent interest, is that any planar domain can be equilaterally triangulated with triangles whose diameters (at any prescribed rate) near .
Keywords
Cite
@article{arxiv.2202.02410,
title = {Equilateral Triangulations and The Postcritical Dynamics of Meromorphic Functions},
author = {Christopher J. Bishop and Kirill Lazebnik and Mariusz Urbański},
journal= {arXiv preprint arXiv:2202.02410},
year = {2022}
}