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

Osborne, J. W. (2013). Spiders' webs and locally connected Julia sets of transcendental entire functions. Ergodic Theory and Dynamical Systems, 33(04) pp. 1146–1161.

DOI: https://doi.org/10.1017/S0143385712000259

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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