Perturbations of graphs for Newton maps I: bounded hyperbolic components
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Published:2022-08-31
Issue:
Volume:
Page:1-29
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ISSN:0143-3857
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Container-title:Ergodic Theory and Dynamical Systems
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language:en
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Short-container-title:Ergod. Th. Dynam. Sys.
Author:
GAO YAN,NIE HONGMING
Abstract
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.
Funder
National Natural Science Foundation of China
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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