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newton graphs

Ergodic Theory and Dynamical Systems (1)

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Perturbations of graphs for Newton maps I: bounded hyperbolic components
Part of
- Complex dynamical systems
YAN GAO, HONGMING NIE
Journal:

Ergodic Theory and Dynamical Systems / Volume 43 / Issue 9 / September 2023

Published online by Cambridge University Press:

31 August 2022, pp. 2997-3025

Print publication:

September 2023
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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.