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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2010

On the topology of wandering Julia components

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Résumé

It is known that for a rational map ƒ with a disconnected Julia set, the set of wandering Julia components is uncountable. We prove that all but countably many of them have a simple topology, namely having one or two complementary components. We show that the remaining countable subset Σ is backward invariant. Conjecturally Σ does not contain an infinite orbit. We give a very strong necessary condition for Σ to contain an infinite orbit, thus proving the conjecture for many different cases. We provide also two sufficient conditions for a Julia component to be a point. Finally we construct several examples describing different topological structures of Julia components.

Dates et versions

hal-03031619 , version 1 (30-11-2020)

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Guizhen Cui, Wenjuan Peng, Lei Tan. On the topology of wandering Julia components. Discrete and Continuous Dynamical Systems - Series A, 2010, 29 (3), pp.929 - 952. ⟨10.3934/dcds.2011.29.929⟩. ⟨hal-03031619⟩
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