arXiv:1911.09406 Abstract | arXiv Analytics

arXiv:1911.09406 [math.DS]Abstract References Reviews Resources

Perturbations of graphs for Newton maps

Published 2019-11-21Version 1

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.

Comments: 23 pages

Categories: math.DS

Keywords: hyperbolic component, perturbations, quartic newton maps, degenerating newton maps, sufficient condition

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