Eremenko, A. E. On the iteration of entire functions. (English) Zbl 0692.30021 Dynamical systems and ergodic theory, 28th Sem. St. Banach Int. Math. Cent., Warsaw/Pol. 1986, Banach Cent. Publ. 23, 339-345 (1989). [For the entire collection see Zbl 0686.00015.] Denote by \(f^ n\) the \(n\)-th iterate of an entire function \(f\). The properties of the set \(I(f)=\{z\in {\mathbb{C}}:\) \(f^ nz\to \infty \}\) are studied. The main result is that \(I(f)\) is not empty for every nonlinear entire function \(f\). The proof is based on the Wiman-Valiron theory. Reviewer: A.E.Eremenko Cited in 10 ReviewsCited in 56 Documents MSC: 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 60E05 Probability distributions: general theory 37F50 Small divisors, rotation domains and linearization in holomorphic dynamics 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets Keywords:iterate of an entire function Citations:Zbl 0686.00015 PDFBibTeX XML