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Additional info for Advanced Course Of Mathematical Analysis III: Proceedings of the Third International School La Rabida, Spain, 3 - 7 September 2007
Let f ∈ End (C, 0) be a holomorphic local dynamical system of multiplier λ = e2πiθ ∈ S 1 with θ ∈ / Q. Then f is formally conjugated to its linear part. Proof. We shall prove that there is a unique formal power series h(z) = z + h2 z 2 + · · · ∈ C[[z]] May 6, 2008 15:45 22 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 M. Abate such that h(λz) = f (h(z)). Indeed, we have h(λz) − f (h(z)) = (λj − λ)hj − aj z j − = j≥2 = j≥2 j =1 j hk z k−2 z +j k≥2 (λj − λ)hj − aj − Xj (h2 , .
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