Functional Analysis and Its Applications

, Volume 43, Issue 1, pp 78–80 | Cite as

Formal and analytic linearizability of families of conformal map germs (ℂ, 0) → (ℂ, 0)

  • A. Yu. Fishkin
Brief Communications


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 words

conformal map germ local family resonance term normal form multiplier small denominators analytic conjugation 


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  1. [1]
    L. Carleson and T. W. Gamelin, Complex Dynamics, Springer-Verlag, New York, 1993.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Independent University of MoscowMoscowRussia

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