We 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<∞ 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.
A bound on the number of rationally invisible repelling orbits / Benini, A.; Fagella, N.. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 370(2020), p. 107214. [10.1016/j.aim.2020.107214]
|Appare nelle tipologie:||1.1 Articolo su rivista|