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Holomorphic motions, Fatou linearization, and quasiconformal rigidity for parabolic germs
2009
The Michigan mathematical journal
By applying holomorphic motions, we prove that a parabolic germ is quasiconformal rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near conformal as long as we consider these germs defined on smaller and smaller neighborhoods. Before to prove this theorem, we use the idea of holomorphic motions to give a conceptual proof of the Fatou linearization theorem. As a byproduct, we also prove that any
doi:10.1307/mmj/1250169075
fatcat:c4pgodp2z5bq7fsolrf3sry46a