Berretti A., Marmi S.
Limit at Resonances of Linearizations
of Some Complex Analytic Dynamical Systems
(41K, TeX)

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.