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 citeKi00, citeBCLOS16 for polynomials.
Singular values and non-repelling cycles for entire transcendental maps / Benini, A; Fagella, N. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - (2020). [10.1512/iumj.2020.69.8000]
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