Density of hyperbolicity of real Newton maps

Gao, Yan

doi:10.48550/arxiv.1906.03556

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Invariant Graphs For Newton Maps1

Introduction1

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Cited by 2 publications

(2 citation statements)

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“…The dynamics of f can be characterized by an invariant graph that is the so-called Newton graph. Such a graph was first constructed in [4] and then applied to study the dynamics of corresponding maps, see [5,8,9,14,13,29]. In this subsection, we state briefly the construction of Newton graphs and list some properties.…”

Section: Invariant Graphs For Newton Mapsmentioning

confidence: 99%

Perturbations of graphs for Newton maps I: bounded hyperbolic components

Gao

Nie

2022

Ergod. Th. Dynam. Sys.

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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.

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Section: Invariant Graphs For Newton Mapsmentioning

confidence: 99%

Perturbations of graphs for Newton maps I: bounded hyperbolic components

Gao

Nie

2022

Ergod. Th. Dynam. Sys.

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show abstract

“…The dynamics of f can be characterized by an invariant graph what is so-called Newton graph. Such graph was first constructed in [4] and then applied to study the dynamics of corresponding maps, see [5,8,9,13,14,26]. In this subsection, we state briefly the construction of Newton graphs and list some properties.…”

Section: Introductionmentioning

confidence: 99%

Perturbations of graphs for Newton maps

Gao,

Nie

2019

Preprint

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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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Density of hyperbolicity of real Newton maps

Abstract: In this paper, based on the known rigidity theorems of Newton maps ([DS], [RYZ]) and real polynomials ([KSS1], [CvS]), we prove the density of hyperbolicity in the family of real Newton maps of degree d ≥ 3 with all free critical points real.

Cited by 2 publications

References 8 publications

Perturbations of graphs for Newton maps I: bounded hyperbolic components

Perturbations of graphs for Newton maps I: bounded hyperbolic components

Perturbations of graphs for Newton maps

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