Submitted by ims_edit on Thu, 08/03/2023 - 11:53
preprint-id:
ims23-03
preprint-title:
Bounded Fatou and Julia components of meromorphic functions
preprint-abstract:
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 continua using approximation theory.
preprint-year:
2023