Abstract
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.
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References
L. Carleson and T. W. Gamelin, Complex Dynamics, Springer-Verlag, New York, 1993.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 43, No. 1, pp. 94–96, 2009
Original Russian Text Copyright © by A. Yu. Fishkin
Supported in part by RFBR project 7-01-00017-a and joint RFBR/CNRS project 05-01-02801-CNRS_a.
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Fishkin, A.Y. Formal and analytic linearizability of families of conformal map germs (ℂ, 0) → (ℂ, 0). Funct Anal Its Appl 43, 78–80 (2009). https://doi.org/10.1007/s10688-009-0011-4
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DOI: https://doi.org/10.1007/s10688-009-0011-4