×

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
PDF BibTeX XML Cite
Full Text: EuDML EMIS