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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164373
A bound on the number of rationally invisible repelling orbits
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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 $q<\infty$ 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.
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BENINI, Anna Miriam and FAGELLA RABIONET, Núria. A bound on the number of rationally invisible repelling orbits. Advances in Mathematics. 2020. Vol. 370. ISSN 0001-8708. [consulted: 14 of June of 2026]. Available at: https://hdl.handle.net/2445/164373