96-428 Berretti A., Marmi S.

Limit at Resonances of Linearizations of Some Complex Analytic Dynamical Systems (41K, TeX) Sep 20, 96

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Abstract. We consider the behaviour near resonances of linearizations of=20 germs of holomorphic diffeomorphisms of (C,0) and of=20 the semi-standard map.=20 We prove that there exists suitable scalings under which the=20 linearizations converge uniformly to some analytic function as the=20 multiplier, or rotation number, tends non-tangentially to a=20 resonance. This limit functions are computed analytically in the case=20 of germs and are related to the formal classifications of germs with a=20 parabolic fixed point. In the semi-standard map case we give a=20 heuristic argument to compute the limit.

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