Limit functions in wandering domains of meromorphic functions. (English) Zbl 1019.37027

Let \(f\) be a function which is meromorphic outside a sufficiently small, nonempty totally disconnected compact set of essential singularities, and \(U\) be a wandering component of the Fatou set of \(f\). The author proves that any limit function of a subsequence of iterates of \(f\) in \(U\) is a constant which lies in the derived set of the forward orbit of the set of singular points of the inverse of \(f\).


37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
30D30 Meromorphic functions of one complex variable (general theory)
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
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