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Wandering domains for composition of entire functions

Fagella, Núria ; Godillon, Sébastian ; Jarque, Xavier

Journal of mathematical analysis and applications, 2015-09, Vol.429 (1), p.478-496 [Periódico revisado por pares]

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Título:
Wandering domains for composition of entire functions
Autor: Fagella, Núria ; Godillon, Sébastian ; Jarque, Xavier
Assuntos: Entire functions ; Entire maps ; Ergodic theory ; Funcions enteres ; Holomorphic dynamics ; Polinomis ; Polynomials ; Quasiconformal maps ; Teoria ergòdica ; Wandering domains
É parte de: Journal of mathematical analysis and applications, 2015-09, Vol.429 (1), p.478-496
Descrição: C. Bishop in [10, Theorem 17.1] 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 in [22, Theorem 4] and results of W. Bergweiler and A. Hinkkanen in [6] related to this problem.
Editor: Elsevier Inc
Idioma: Inglês

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