An algebraic formulation of Thurston's characterization of rational functions

Details An algebraic formulation of Thurston's characterization of rational functions An algebraic formulation of Thurston's characterization of rational functions

2007-08-24

arxiv.org/abs/0708.3385v2

Mathematics

Dynamical Systems

33 pages; substantially revised

Scientific paper

Following Douady-Hubbard and Bartholdi-Nekrashevych, we give an algebraic formulation of Thurston's characterization of rational functions. The techniques developed are applied to the analysis of the dynamics on the set of free homotopy classes of simple closed curves induced by a rational function. The resulting finiteness results yield new information on the global dynamics of the pullback map on Teichm\"uller space used in the proof of the characterization theorem.

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