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Accepted version

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2014-02-08

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/63074

On the Connectivity of the Julia sets of meromorphic functions

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http://dx.doi.org/10.1007/s00222-014-0504-5

Abstract

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Subject

Funcions enteres, Funcions de variables complexes

Subject (English)

Entire functions, Functions of complex variables

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Articles publicats en revistes (Matemàtiques i Informàtica)

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BARANSKI, Krzysztof, et al. On the Connectivity of the Julia sets of meromorphic functions. Inventiones Mathematicae. 2014. Vol. 198, num. 3, pags. 591-636. ISSN 0020-9910. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/63074

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