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.