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Title: Classifying simply connected domains
Author: Benini, Anna Miriam
Evdoridou, Vasiliki
Fagella Rabionet, Núria
Rippon, Philip J.
Stallard, Gwyneth M.
Keywords: Sistemes dinàmics diferenciables
Funcions de variables complexes
Differentiable dynamical systems
Functions of complex variables
Issue Date: Aug-2022
Publisher: Springer Verlag
Abstract: While the dynamics of transcendental entire functions in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected wandering domains have so far eluded classification. We give a detailed classification of the dynamics in such wandering domains in terms of the hyperbolic distances between iterates and also in terms of the behaviour of orbits in relation to the boundaries of the wandering domains. In establishing these classifications, we obtain new results of wider interest concerning non-autonomous forward dynamical systems of holomorphic self maps of the unit disk. We also develop a new general technique for constructing examples of bounded, simply connected wandering domains with prescribed internal dynamics, and a criterion to ensure that the resulting boundaries are Jordan curves. Using this technique, based on approximation theory, we show that all of the nine possible types of simply connected wandering domain resulting from our classifications are indeed realizable.
Note: Versió postprint del document publicat a:
It is part of: Mathematische Annalen, 2022, vol.383, num. 3-4, p. 1127-1178
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ISSN: 0025-5831
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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