  We introduce a topological object, called hairy Cantor set, which in many
ways enjoys the universal features of objects like Jordan curve, Cantor set,
Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation
of hairy Cantor sets, and prove that any two such objects in the plane are
ambiently homeomorphic.
  Hairy Cantor sets appear in the study of the dynamics of holomorphic maps
with infinitely many renormalisation structures. They are employed to link the
fundamental concepts of polynomial-like renormalisation by Douady-Hubbard with
the arithmetic conditions obtained by Herman-Yoccoz in the study of the
dynamics of analytic circle diffeomorphisms.
