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Perturbations of graphs for Newton maps I: bounded hyperbolic components
Published online by Cambridge University Press: 31 August 2022
Abstract
We consider graphs consisting of finitely many internal rays for degenerating Newton maps and state a convergence result. As an application, we prove that a hyperbolic component in the moduli space of quartic Newton maps is bounded if and only if every element has degree $2$ on the immediate basin of each root. This provides the first complete description of bounded hyperbolic components in a complex two-dimensional moduli space.
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- © The Author(s), 2022. Published by Cambridge University Press
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