Formal and analytic linearizability of families of conformal map germs (ℂ, 0) → (ℂ, 0)
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We consider a nondegenerate one-parameter family of germs of conformal maps of (ℂ, 0) into (ℂ, 0). We prove that such a family is analytically linearizable whenever it is formally linearizable. In this case, the linearizing coordinate change analytically depends on the parameter.
Key wordsconformal map germ local family resonance term normal form multiplier small denominators analytic conjugation
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