NON-REAL PERIODIC POINTS OF ENTIRE FUNCTIONS

ABSTRACT. It is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n 2, then f has infinitely many repelling periodic points of period n that do not lie on l. 1. Introduction and main result. Let f be an entire function and denote by f n its n-th iterate. We say that z0 is a periodic point of f if f n(z0) = z0 for some n 2 N. The smallest n with this property is called the period of z0. A periodic point z0 of period n is called attracting, indifferent, or repelling depending on whether j(f n)0(z0)j is less than, equal to, or greater than 1. The following results were proved in [2] and [3]