Perturbations of graphs for Newton maps

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 $2$ on the immediate basin of each root.

23 pages

References in corpus (2)

• Bounded hyperbolic components of bicritical rational maps
• Density of hyperbolicity of real Newton maps