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arXiv:1110.3256 [math.DS]AbstractReferencesReviewsResources

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

J. W. Osborne

Published 2011-10-14, updated 2012-03-26Version 2

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.

Comments: 17 pages. v2: some corrections and improvements of a minor nature; to appear in Ergodic Theory Dynam. Systems
Categories: math.DS, math.CV
Subjects: 37F10, 30D05
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