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arXiv · 1712.00273

Singular values and non-repelling cycles for entire transcendental maps

Anna Miriam Benini·Núria Fagella
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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. Our approach is combinatorial in the spirit of the approach used by [Ki00], [BCL+16] for polynomials.

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Anna Miriam Benini, Núria Fagella. 2017-12-01. Singular values and non-repelling cycles for entire transcendental maps. https://arxiv.org/abs/1712.00273

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