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Entire functions for which the escaping set is a spider's web

Published online by Cambridge University Press:  05 September 2011

D. J. SIXSMITH
D. J. SIXSMITH*
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA. e-mail: [email protected]
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Abstract

We construct several new classes of transcendental entire functions, f, such that both the escaping set, I(f), and the fast escaping set, A(f), have a structure known as a spider's web. We show that some of these classes have a degree of stability under changes in the function. We show that new examples of functions for which I(f) and A(f) are spiders' webs can be constructed by composition, by differentiation, and by integration of existing examples. We use a property of spiders' webs to give new results concerning functions with no unbounded Fatou components.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 3 , November 2011 , pp. 551 - 571
Copyright
Copyright © Cambridge Philosophical Society 2011

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