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Non-normality, topological transitivity and expanding families

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  14 December 2021

THIERRY MEYRATH  and
JÜRGEN MÜLLER
THIERRY MEYRATH
Affiliation:
University of Luxembourg, Department of Mathematics, L-4364 Esch-sur-Alzette, Luxembourg. e-mail: thierry.meyrath@uni.lu
JÜRGEN MÜLLER
Affiliation:
Universität Trier, Fachbereich IV – Mathematik, D-54286 Trier, Germany. e-mail: jmueller@uni-trier.de
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Abstract

We investigate the behaviour of families of meromorphic functions in the neighbourhood of points of non-normality and prove certain covering properties that complement Montel’s Theorem. In particular, we also obtain characterisations of non-normality in terms of such properties.

MSC classification

Primary: 30D45: Bloch functions, normal functions, normal families 30D30: Meromorphic functions, general theory
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 173 , Issue 3 , November 2022 , pp. 511 - 523
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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