Abstract

Let f be a transcendental entire function and let I(f) be the points which escape to infinity under iteration. Bergweiler and Hinkkanen introduced the fast escaping sets A(f) and subsequently, Rippon and Stallard introduced `Levels' of fast escaping sets . These sets under some restriction have the properties of "infinite spider's web" structure. Here we give some topological properties of the infinite spider's web and show some of the transcendental entire functions whose levels of the fast escaping sets have infinite spider's web structure.

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