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On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points I
Author(s) -
Fagella Núria,
Jarque Xavier,
Taixés Jordi
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdn012
Subject(s) - julia set , mathematics , meromorphic function , newton fractal , transcendental number , fixed point , entire function , polynomial , pure mathematics , multiplier (economics) , preprint , discrete mathematics , mathematical analysis , algorithm , local convergence , iterative method , world wide web , computer science , economics , macroeconomics
It is known that the Julia set of the Newton method of a non‐constant polynomial is connected (Mitsuhiro Shishikura, Preprint, 1990, M/90/37, Inst. Hautes Études Sci. ). 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 meromorphic functions; that is, we show the existence of such fixed points, provided that immediate attractive basins or preperiodic components are multiply connected.