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2018-08-27

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/125727

Connectivity of Julia sets of Newton maps: a unified approach

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https://doi.org/10.4171/RMI/1022

Abstract

In this paper we present a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function on the complex plane (a polynomial of degree larger than $1$ or a transcendental entire function) is connected. The result was recently completed by the authors' previous work, as a consequence of a more general theorem whose proof spreads among many papers, which consider separately a number of particular cases for rational and transcendental maps, and use a variety of techniques. In this note we present a unified, direct and reasonably self-contained proof which works in all situations alike.

Subject

Funcions enteres, Sistemes dinàmics complexos, Superfícies de Riemann

Subject (English)

Entire functions, Complex dynamical systems, Riemann surfaces

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

BARANSKI, Krzysztof, et al. Connectivity of Julia sets of Newton maps: a unified approach. Revista Matematica Iberoamericana. 2018. Vol. 34, num. 3, pags. 1211-1228. ISSN 0213-2230. [consulted: 18 of August of 2026]. Available at: https://hdl.handle.net/2445/125727

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