Classifying simply connected wandering domains
Benini, Anna Miriam (Università di Parma. Department of Mathematical, Physical and Computer Sciences)
Evdoridou, Vasiliki (The Open University. School of Mathematics and Statistics (UK))
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Rippon, Philip J. (The Open University. School of Mathematics and Statistics (UK))
Stallard, Gwyneth M. (The Open University. School of Mathematics and Statistics (UK))

Date:	2022
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.
Grants:	European Commission 703269 Agencia Estatal de Investigación MTM2017-86795-C3-3-P Ministerio de Economía y Competitividad MDM-2014-0445 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Mathematische Annalen, Vol. 383, Issue 3-4 (August 2022) , p. 1127-1178, ISSN 1432-1807

DOI: 10.1007/s00208-021-02252-0

52 p, 2.2 MB

Postprint 48 p, 1022.2 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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