Resumen de Spiders’ webs of doughnuts

Alastair Fletcher, Daniel Stoertz

• If f:R3→R3 is a uniformly quasiregular mapping with Julia set J(f), a genus g Cantor set, for g≥1, then for any linearizer L at any repelling periodic point of f, the fast escaping set A(L) consists of a spiders' web structure containing embedded genus g tori on any sufficiently large scale. In other words, A(L) 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 f:Rn→Rn is a uniformly quasiregular mapping, for n≥2, and J(f) is a Cantor set, then every periodic point is in J(f) and is repelling.