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Title: | A bound on the number of rationally invisible repelling orbits |
Author: | Benini, Anna Miriam Fagella Rabionet, Núria |
Keywords: | Sistemes dinàmics complexos Sistemes dinàmics hiperbòlics Complex dynamical systems Hyperbolic dynamical systems |
Issue Date: | 26-Aug-2020 |
Publisher: | Elsevier B.V. |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.aim.2020.107214 |
It is part of: | Advances in Mathematics, 2020, vol. 370 |
URI: | http://hdl.handle.net/2445/164373 |
Related resource: | https://doi.org/10.1016/j.aim.2020.107214 |
ISSN: | 0001-8708 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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