Geodesic
Formal and Analytic Linearizability of Families of Conformal Map Germs
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 94-96

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We consider a nondegenerate one-parameter family of germs of conformal maps of $(\mathbb{C}, 0)$ into $(\mathbb{C}, 0)$. 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.
Mots-clés : conformal map germ, multiplier, analytic conjugation.
Keywords: local family, resonance term, normal form, small denominators 
@article{FAA_2009_43_1_a9,
     author = {A. Yu. Fishkin},
     title = {Formal and {Analytic} {Linearizability} of {Families} of {Conformal} {Map} {Germs}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {94--96},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_1_a9/}
}
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A. Yu. Fishkin. Formal and Analytic Linearizability of Families of Conformal Map Germs. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 94-96. http://geodesic.mathdoc.fr/item/FAA_2009_43_1_a9/