Spiders’ webs of doughnuts

• Alastair Fletcher ^[1] ; Daniel Stoertz ^[1]
  1. [1] Northern Illinois University

     Northern Illinois University

     Township of DeKalb, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 1, 2021, págs. 161-176
• Idioma: inglés
• DOI: 10.4171/rmi/1204
• Enlaces
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• Resumen

  • 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.