If is a uniformly quasiregular mapping with Julia set , a genus Cantor set, for , then for any linearizer at any repelling periodic point of , the fast escaping set consists of a spiders' web structure containing embedded genus tori on any sufficiently large scale. In other words, contains a spiders' web of doughnuts. This type of structure is specific to higher dimensions, and cannot happen for the fast escaping set of a transcendental entire function in the plane. We also show that if is a uniformly quasiregular mapping, for , and is a Cantor set, then every periodic point is in and is repelling.
Cite this article
Alastair Fletcher, Daniel Stoertz, Spiders’ webs of doughnuts. Rev. Mat. Iberoam. 37 (2021), no. 1, pp. 161–176DOI 10.4171/RMI/1204