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Spiders’ webs and locally connected Julia sets of transcendental entire functions

Published online by Cambridge University Press:  18 July 2012

J. W. OSBORNE
J. W. OSBORNE*
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK (email: j.osborne@open.ac.uk)
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Abstract

We show that if the Julia set of a transcendental entire function is locally connected, then it takes the form of a spider’s web in the sense defined by Rippon and Stallard. In the opposite direction, we prove that a spider’s web Julia set is always locally connected at a dense subset of buried points. We also show that the set of buried points (the residual Julia set) can be a spider’s web.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 4 , August 2013 , pp. 1146 - 1161
Copyright
Copyright © 2012 Cambridge University Press 

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