## 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 $$f$$.

### MSC:

 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

### Keywords:

singularities; Fatou set; orbit; singular points
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