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Ufimskii Matematicheskii Zhurnal, 2011, Volume 3, Issue 3, Pages 120–126
(Mi ufa107)
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This article is cited in 1 scientific paper (total 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.
Received: 28.06.2011
Citation:
Zh. G. Rakhmatullina, “The Fatou set of an entire function with the Fejér gaps”, Ufimsk. Mat. Zh., 3:3 (2011), 120–126
Linking options:
https://www.mathnet.ru/eng/ufa107 https://www.mathnet.ru/eng/ufa/v3/i3/p120
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Abstract page: | 238 | Full-text PDF : | 101 | References: | 49 | First page: | 2 |
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