Brief communications

Formal and Analytic Linearizability of Families of Conformal Map Germs $(\mathbb{C},0)\to(\mathbb{C},0)$

A. Yu. Fishkin

Independent University of Moscow

Abstract: 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.

Keywords: conformal map germ, local family, resonance term, normal form, multiplier, small denominators, analytic conjugation.

UDC: 517.547.3

Received: 25.09.2007

DOI: 10.4213/faa2945

 English version: Functional Analysis and Its Applications, 2009, 43:1, 78–80

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