Perturbations of graphs for Newton maps
Dynamical Systems
2019-11-22 v1
Abstract
We study the convergence of graphs consisting of finitely many internal rays for degenerating Newton maps. We state a sufficient condition to guarantee the convergence. As an application, we investigate the boundedness of hyperbolic components in the moduli space of quartic Newton maps. We prove that such a hyperbolic component is bounded if and only if every element has degree on the immediate basin of each root.
Cite
@article{arxiv.1911.09406,
title = {Perturbations of graphs for Newton maps},
author = {Yan Gao and Hongming Nie},
journal= {arXiv preprint arXiv:1911.09406},
year = {2019}
}
Comments
23 pages