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Singular values and non-repelling cycles for entire transcendental maps

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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.

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Indiana University Mathematics Journal, 2020, vol. 69, p. 1543-1558

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(c) Indiana University Mathematics Journal, 2020

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Singular values and non-repelling cycles for entire transcendental maps