Wandering Julia components of cubic rational maps
Guizhen Cui, Wenjuan Peng, Luxian Yang
TL;DR
This paper proves that wandering Julia components in cubic rational maps are limited in complexity, having at most two complementary components, which advances understanding of their topological structure.
Contribution
It establishes a new topological constraint on wandering Julia components in cubic rational maps, showing they cannot have more than two complementary components.
Findings
Wandering Julia components have at most two complementary components.
The result applies specifically to cubic rational maps.
It provides new insights into the topology of Julia sets.
Abstract
We prove that every wandering Julia component of cubic rational maps eventually has at most two complementary components.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions