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Normalization of almost conformal parabolic germs. (English) Zbl 0824.30016

Almost conformal (AC) germs of homeomorphisms are considered. Almost conformality means that the Beltrami coefficient of the germ is flat at the origin. The main question is when two such germs are the same up to a change of variable which is an AC germ itself. As usually hyperbolic germs are all equivalent to linear ones. Here the case of parabolic germs is under investigation. The space of moduli of parabolic AC germs is constructed. This is similar to the classical case of classification of parabolic holomorphic germs, now asymptotically holomorphic functions are involved in the description. A new effect of vertical AC equivalency appears.

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
26A18 Iteration of real functions in one variable
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