Illinois Journal of Mathematics

Singularities and wandering domains in iteration of meromorphic functions

Jian-Hua Zheng

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Let $f$ be a transcendental meromorphic function and let $U$ be a wandering domain of $f$. Under some conditions, we prove that a finite limit function of $\{f^{n}\}$ on $U$ is in the derived set of the forward orbit of the set sing $(f^{-1})$ of singularities of the inverse function of $f$. The existence of $\{n_{k}\}$ such that $f^{n_k}}|_{U}$ tends to $\infty$ is also considered when $f$ is entire. If sing$(f^{-l})$ is bounded, however, we show that $\{f^{n}(z)\}_{n=o}^\infty$ in $F(f)$ does not tend to $\infty$.

Article information

Illinois J. Math., Volume 44, Issue 3 (2000), 520-530.

First available in Project Euclid: 20 October 2009

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Zentralblatt MATH identifier

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets


Zheng, Jian-Hua. Singularities and wandering domains in iteration of meromorphic functions. Illinois J. Math. 44 (2000), no. 3, 520--530. doi:10.1215/ijm/1256060412.

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