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arXiv · 1911.09406

Perturbations of graphs for Newton maps

Yan Gao·Hongming Nie
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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.

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Yan Gao, Hongming Nie. 2019-11-21. Perturbations of graphs for Newton maps. https://arxiv.org/abs/1911.09406

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