This article is cited in 1 paper

The Fatou set of an entire function with the Fejér gaps

Zh. G. Rakhmatullina

Bashkir State University, Ufa, Russia

Abstract: The paper considers the Fatou set of an entire transcendental function, i.e. the largest open set of the complex plane where the family of iterations of the given function forms a normal family. We assume that the entire function, in general, is of an infinite order. We give the sufficient condition on the indexes of the series (it is stronger than the Fejér gap condition), under which every component of the Fatou set is bounded. The same result under stronger restrictions was earlier obtained by Yu. Wang.

Keywords: entire functions, Fejér gaps, iterations of functions, Fatou set.

UDC: 517.53

Received: 28.06.2011

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