# Singular values and non-repelling cycles for entire transcendental maps

##
Anna Miriam Benini

created by risa on 17 Jan 2018

23 jan 2018
-- 16:00

Aula D'Antoni, Dip.Matematica, Università "Tor Vergata", Roma

**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 $\text{[Ki00]}$, $\text{[BCL+16]}$ for polynomials