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On the topology of wandering Julia components

Abstract :

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.

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Soumis le : lundi 30 novembre 2020 - 15:21:14
Dernière modification le : mercredi 20 octobre 2021 - 03:19:01

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



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