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Topological and analytical conjugacy of non-commutative groups of germs of conformal mappings. (Russian. English summary) Zbl 0568.30010

The author establishes (theorem 1) that: ”for insoluble groups of conformal mapping germs with superposition operation the topological conjugacy coincides with the analytical ones” in more general hypotheses than Yu. S. Il’yashenko’s [ibid. 4, 83-136 (1978; Zbl 0418.34007)] theorem 6 and, as consequence, the author improves Yu. S. Il’yashenko’s theorem 3 (in the paper quoted above) on absolute structural instability of analytical differential equations in the complex projective plane. Finally, by means of the method used for proving his theorem 1, the author establishes a relation between the functional module corresponding to the formal and analytic classification of the germs of conformal mappings with identical linear part and also a theorem [analogous to those obtained by J. Ecalle in J. Math. Pure Appl., IX. Ser. 54, 183-258 (1975; Zbl 0285.26010)] on the analytic dependence of the functional module on the parameter, when the conformal mapping germ depends analytically on the parameter.
Reviewer: P.Caraman

MSC:

30C35 General theory of conformal mappings
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
34M99 Ordinary differential equations in the complex domain
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