Wandering domains for composition of entire functions
C.~Bishop constructs an example of an entire function f in class 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 rel...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:145312 |
| Acceso en línea: | https://ddd.uab.cat/record/145312 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2015.04.020 |
| Access Level: | acceso abierto |
| Palabra clave: | Entire maps Holomorphic dynamics Quasiconformal maps Wandering domains |
| Sumario: | C.~Bishop constructs an example of an entire function f in class 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 B such that the Fatou set of f g has a wandering domain, while all Fatou components of f or g are preperiodic. This complements a result of A.~Singh and results of W.~Bergweiler and A.Hinkkanen related to this problem. |
|---|