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Fatou's web


Author: V. Evdoridou
Journal: Proc. Amer. Math. Soc. 144 (2016), 5227-5240
MSC (2010): Primary 37F10; Secondary 30D05
DOI: https://doi.org/10.1090/proc/13150
Published electronically: June 3, 2016
MathSciNet review: 3556267
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Abstract: Let $ f$ be Fatou's function, that is, $ f(z)= z+1+e^{-z}$. We prove that the escaping set of $ f$ has the structure of a `spider's web', and we show that this result implies that the non-escaping endpoints of the Julia set of $ f$ together with infinity form a totally disconnected set. We also present a well-known transcendental entire function, due to Bergweiler, for which the escaping set is a spider's web, and we point out that the same property holds for some families of functions.


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Additional Information

V. Evdoridou
Affiliation: Department of Mathematics and Statistics, Walton Hall, The Open University, Milton Keynes MK7 6AA, United Kingdom
Email: vasiliki.evdoridou@open.ac.uk

DOI: https://doi.org/10.1090/proc/13150
Received by editor(s): October 26, 2015
Received by editor(s) in revised form: February 4, 2016, and February 11, 2016
Published electronically: June 3, 2016
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2016 American Mathematical Society