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2020-06-01

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/172530

Singular values and non-repelling cycles for entire transcendental maps

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https://doi.org/10.1512/iumj.2020.69.8000

Abstract

Let $f$ be a map with bounded set of singular values for which periodic dynamic rays exist and land. We prove that each non-repelling cycle is associated to a singular orbit which cannot accumulate on any other non-repelling cycle. When $f$ has finitely many singular values this implies a refinement of the Fatou-Shishikura inequality.

Subject

Sistemes dinàmics diferenciables, Funcions de variables complexes, Equacions funcionals

Subject (English)

Differentiable dynamical systems, Functions of complex variables, Functional equations

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Articles publicats en revistes (Matemàtiques i Informàtica)
Publicacions de projectes de recerca finançats per la UE

Citation

BENINI, Anna Miriam and FAGELLA RABIONET, Núria. Singular values and non-repelling cycles for entire transcendental maps. Indiana University Mathematics Journal. 2020. Vol. 69, num. 1543-1558. ISSN 0022-2518. [consulted: 12 of June of 2026]. Available at: https://hdl.handle.net/2445/172530

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