Wandering domains for composition of entire functions
C. Bishop in [Bis, Theorem 17.1] constructs an example of an entire function $f$ in class $\mathcal {B}$ with at least two grand orbits of oscillating wandering domains. In this paper we show that his example has exactly two such orbits, that is, $f$ has no unexpected wandering domains. We apply thi...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/97100 |
| Acceso en línea: | https://hdl.handle.net/2445/97100 |
| Access Level: | acceso abierto |
| Palabra clave: | Polinomis Teoria ergòdica Funcions enteres Polynomials Ergodic theory Entire functions |
| Sumario: | C. Bishop in [Bis, Theorem 17.1] constructs an example of an entire function $f$ in class $\mathcal {B}$ with at least two grand orbits of oscillating wandering domains. In this paper we show that his example has exactly two such orbits, that is, $f$ has no unexpected wandering domains. We apply this result to the classical problem of relating the Julia sets of composite functions with the Julia set of its members. More precisely, we show the existence of two entire maps $f$ and $g$ in class $\mathcal {B}$ such that the Fatou set of $f \circ g$ has a wandering domain, while all Fatou components of $f$ or $g$ are preperiodic. This complements a result of A. Singh in [Sin03, Theorem 4] and results of W. Bergweiler and A.Hinkkanen in [BH99] related to this problem. |
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