Document type
ArticleVersion
Accepted versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/97100
Wandering domains for composition of entire functions
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
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.
Subject
Subject (English)
Citation
Citation
FAGELLA RABIONET, Núria, GODILLON, Sébastien and JARQUE I RIBERA, Xavier. Wandering domains for composition of entire functions. Journal of Mathematical Analysis and Applications. 2015. Vol. 429, num. 1, pags. 478-496. ISSN 0022-247X. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/97100