Thurston equivalence of topological polynomials
  We answer Hubbard's question on determining the Thurston equivalence class of ``twisted rabbits'', i.e. images of the ``rabbit'' polynomial under n-th powers of the Dehn twists about its ears.   The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points.   In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions. 
Laurent Bartholdi, Volodymyr Nekrashevych