# This Collection

By Defense Date By Authors By Titles By Subject

# Statistics

View Statistics All RECERCAT

# My RECERCAT

 Title: Wandering domains for composition of entire functions Fagella Rabionet, Núria; Godillon, Sébastien; Jarque i Ribera, Xavier Universitat de Barcelona 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. PolinomisTeoria ergòdicaFuncions enteresPolynomialsErgodic theoryEntire functions cc-by-nc-nd (c) Elsevier, 2015 info:eu-repo/semantics/embargoedAccess http://creativecommons.org/licenses/by-nc-nd/3.0/es Articleinfo:eu-repo/semantics/acceptedVersion Elsevier

# Related documents

## Other documents of the same author

Devaney, Robert L.; Fagella Rabionet, Núria; Garijo Real, Antonio; Jarque i Ribera, Xavier
Devaney, Robert L.; Fagella Rabionet, Núria; Garijo Real, Antonio; Jarque i Ribera, Xavier
Baranski, Krzysztof; Fagella Rabionet, Núria; Jarque i Ribera, Xavier; Karpinska, Boguslava
Jarque i Ribera, Xavier
Campos, Beatriz; Garijo, Antonio; Jarque i Ribera, Xavier; Vindel, Pura

Coordination

Supporters