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Thurston equivalence of topological polynomials

Laurent Bartholdi·Volodymyr Nekrashevych
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Abstract

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.

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Laurent Bartholdi, Volodymyr Nekrashevych. 2005-10-04. Thurston equivalence of topological polynomials. https://doi.org/10.1007/s11511-006-0007-3

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