Article ID Journal Published Year Pages File Type
4615295 Journal of Mathematical Analysis and Applications 2015 19 Pages PDF
Abstract

C. Bishop in [10, Theorem 17.1] constructs an example of an entire function f   in class BB 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 BB such that the Fatou set of f∘gf∘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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
, , ,