A bound on the number of rationally invisible repelling orbits
| Autor: | Núria Fagella, Anna Miriam Benini |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Bounded set General Mathematics 010102 general mathematics Function (mathematics) Sistemes dinàmics complexos Accessibility 01 natural sciences Singular value Sistemes dinàmics hiperbòlics 37F10 30D05 0103 physical sciences Periodic orbits Fatou-Shishikura inequality Complex dynamical systems Holomorphic dynamics 010307 mathematical physics Transcendental number Transcendental maps Hyperbolic dynamical systems 0101 mathematics Mathematics - Dynamical Systems Mathematics |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Dipòsit Digital de la UB Universidad de Barcelona Recercat. Dipósit de la Recerca de Catalunya instname Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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