Infinite limits in the iteration of entire functions

Abstract

AbstractIf f is a transcendental entire function and D is a non-wandering component of the set of normality of the iterates of f such that fn → ∞ in D then log |fn(z)| = O(n) as n → ∞ for z in D. For a wandering component the convergence of fn to ∞ in D may be arbitrarily fast.