Wandering domains for composition of entire functions

作者：Fagella Nuria; Godillon Sebastian; Jarque Xavier^*

来源：Journal of Mathematical Analysis and Applications, 2015, 429(1): 478-496.

DOI：10.1016/j.jmaa.2015.04.020

• Quasiconformal maps
• Wandering domains
• Entire maps
• Holomorphic dynamics

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 o 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.

• 出版日期2015-9-1