2004/08/06 by Claudi Meneghin, Meneghin, Claudi
Mathematics · #37F05 #37F25 #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematics and Applications #Meromorphic and Entire Functions #math.CV #msc:37F05 #msc:37F25
paper · pdf · doi:10.48550/arxiv.math/0408083
V4 - revised version (a few typos corrected); French - accepted for publication in the Acta Mathematica Vietnamica
openalex publication_date 2004/08/06 · arxiv created 2011/12/31 · arxiv updated 2012/01/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let g be a holomorphic function in the neighbourhoods of an isolated essential singularity v: if g omits a complex value there, then v may be approached by a sequence of repelling fixed points for g, whose multipliers diverge to ∞. This implies that an entire function omitting a value or a non-Möbius self-map of the punctured plane admit infinite repelling fixed points, whose multipliers diverge to ∞. By another point of view, we show that, if v is not Picard-exceptional for g, then v can be approached by a sequence of 2-cycles of g: these cycles are repelling if v is not a completely branched value.