Hypertranscendency of conjugacies in complex dynamics
type: Item
instance of: scholarly article
title: Hypertranscendency of conjugacies in complex dynamics
zbMATH Open document ID: 0818.30015
DOI: 10.1007/BF01446639
published in: Mathematische Annalen
publication date: 1995-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/165301
review text: The dynamics of rational functions near fixed points are closely connected to the functional equations of Schröder, Böttcher, and Abel. We show that the solutions of these equations are hypertranscendental except in some cases, where they are given in terms of exponential, trigonometric, and elliptic functions. This generalizes earlier work of \textit{J. F. Ritt} [Math. Ann. 95, 671-682 (1926; JFM 52.0321.04)], \textit{F. W. Carroll} [Mich. Math. J. 32, 47-57 (1985; Zbl 0574.30028)], and \textit{P. Borwein} [Proc. Am. Math. Soc. 107, 215-221 (1989; Zbl 0674.39005)].
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 34M99
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 37F99
zbMATH DE Number: 759277
author: P.-G. Becker-Landeck
author: Walter Bergweiler
reviewed by: Walter Bergweiler
MaRDI profile type: Publication
cites work: Q4002072
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description: scientific article; zbMATH DE number 759277