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

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

2011-10-14

arxiv.org/abs/1110.3256v2

Mathematics

Dynamical Systems

17 pages. v2: some corrections and improvements of a minor nature; to appear in Ergodic Theory Dynam. Systems

Scientific paper

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.

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