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2008-04-15

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164190

On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points I

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https://doi.org/10.1112/plms/pdn012

Abstract

It is known that the Julia set of the Newton's method of a non- constant polynomial is connected ([18]). This is, in fact, a consequence of a much more general result that establishes the relationship between simple connectivity of Fatou components of rational maps and fixed points which are repelling or parabolic with multiplier 1. In this paper we study Fatou components of transcendental mero- morphic functions, namely, we show the existence of such fixed points provided that immediate attractive basins or preperiodic components be multiply connected.

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Sistemes dinàmics complexos, Funcions de variables complexes, Funcions meromorfes

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Complex dynamical systems, Functions of complex variables, Meromorphic functions

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Articles publicats en revistes (Matemàtiques i Informàtica)

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FAGELLA RABIONET, Núria, JARQUE I RIBERA, Xavier and TAIXÉS I VENTOSA, Jordi. On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points I. Proceedings of the London Mathematical Society. 2008. Vol. 97, num. 3, pags. 599-622. ISSN 0024-6115. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/164190

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