Thurston equivalence of topological polynomials

Details Thurston equivalence of topological polynomials Thurston equivalence of topological polynomials

2005-10-04

arxiv.org/abs/math/0510082v4

Acta Math. 197 (2006), no. 1, 1--51

Mathematics

Dynamical Systems

40 pages, lots of figures

Scientific paper

10.1007/s11511-006-0007-3

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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