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Bounded Fatou and Julia components of meromorphic functions
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Abstract
We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular. On the other hand, we prove that a planar continuum is a Julia component of some meromorphic function if and only if it has empty interior. We do so by constructing meromorphic functions with wandering compacta using approximation theory.
Springer Science and Business Media LLC
Title: Bounded Fatou and Julia components of meromorphic functions
Description:
Abstract
We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions.
On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular.
On the other hand, we prove that a planar continuum is a Julia component of some meromorphic function if and only if it has empty interior.
We do so by constructing meromorphic functions with wandering compacta using approximation theory.
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