Prescribing the Postsingular Dynamics of Meromorphic Functions
Complex Variables
2019-07-12 v3 Dynamical Systems
Abstract
We show that any dynamics on any discrete planar sequence can be realized by the postsingular dynamics of some transcendental meromorphic function, provided we allow for small perturbations of . This work was influenced by an analogous result of DeMarco, Koch and McMullen for finite in the rational setting. The proof contains a method for constructing meromorphic functions with good control over both the postsingular set of and the geometry of , using the Folding Theorem of Bishop and a classical fixpoint theorem of Tychonoff.
Cite
@article{arxiv.1807.04581,
title = {Prescribing the Postsingular Dynamics of Meromorphic Functions},
author = {Christopher J. Bishop and Kirill Lazebnik},
journal= {arXiv preprint arXiv:1807.04581},
year = {2019}
}