Benini, Anna MiriamFagella Rabionet, Núria2020-06-052022-08-262020-08-260001-8708https://hdl.handle.net/2445/164373We consider entire transcendental maps with bounded set of singular values such that periodic rays exist and land. For such maps, we prove a refined version of the Fatou-Shishikura inequality which takes into account rationally invisible periodic orbits, that is, repelling cycles which are not landing points of any periodic ray. More precisely, if there are $q<\infty$ singular orbits, then the sum of the number of attracting, parabolic, Siegel, Cremer or rationally invisible orbits is bounded above by $q$. In particular, there are at most $q$ rationally invisible repelling periodic orbits. The techniques presented here also apply to the more general setting in which the function is allowed to have infinitely many singular values.application/pdfengcc-by-nc-nd (c) Elsevier B.V., 2020http://creativecommons.org/licenses/by-nc-nd/3.0/esSistemes dinàmics complexosSistemes dinàmics hiperbòlicsComplex dynamical systemsHyperbolic dynamical systemsinfo:eu-repo/semantics/article7013802020-06-05info:eu-repo/semantics/openAccess