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arXiv · 1110.3256

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

J. W. Osborne
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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.

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J. W. Osborne. 2012-03-26. Spiders' webs and locally connected Julia sets of transcendental entire functions. https://arxiv.org/abs/1110.3256

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