Please use this identifier to cite or link to this item:
Title: Wandering domains for composition of entire functions
Author: Fagella Rabionet, Núria
Godillon, Sébastien
Jarque i Ribera, Xavier
Keywords: Polinomis
Teoria ergòdica
Funcions enteres
Ergodic theory
Entire functions
Issue Date: 1-Sep-2015
Publisher: Elsevier
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.
Note: Versió postprint del document publicat a:
It is part of: Journal of Mathematical Analysis and Applications, 2015, vol. 429, num. 1, p. 478-496
Related resource:
ISSN: 0022-247X
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

Files in This Item:
File Description SizeFormat 
659564.pdf358.37 kBAdobe PDFView/Open

This item is licensed under a Creative Commons License Creative Commons