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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 1, Pages 94–96
DOI: https://doi.org/10.4213/faa2945 (Mi faa2945) 		 
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
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DOI: https://doi.org/10.4213/faa2945
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.
Received: 25.09.2007
English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 1, Pages 78–80
DOI: https://doi.org/10.1007/s10688-009-0011-4
Bibliographic databases:
Document Type: Article
UDC: 517.547.3
Language: Russian
Citation: A. Yu. Fishkin, “Formal and Analytic Linearizability of Families of Conformal Map Germs $(\mathbb{C},0)\to(\mathbb{C},0)$”, Funktsional. Anal. i Prilozhen., 43:1 (2009), 94–96; Funct. Anal. Appl., 43:1 (2009), 78–80
Citation in format AMSBIB
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