Computational Methods and Function Theory 6 (2006), No. 1, 77--108
Copyright Heldermann Verlag 2006
Walter Bergweiler
bergweiler@math.uni-kiel.de , Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany.
A heuristic principle attributed to André Bloch says that a family of holomorphic functions is likely to be normal if there are no non-constant entire functions with this property. We discuss this principle and survey recent results that have been obtained in connection with it. We pay special attention to properties related to exceptional values of derivatives and existence of fixed points and periodic points, but we also discuss some other instances of the principle.
Keywords: Normal family, quasinormal, Zalcman Lemma, exceptional value, fixed point, periodic point.
MSC 2000: Primary 30D45; Secondary 30D20, 30D35.
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