Non-linearizability of cubic-perturbed analytic germs at irrationally indifferent fixed points
In this paper, we consider the non-linearizability of analytic germs
with irrationally indifferent fixed points.
Assume that an analytic germ $f$
has an irrationally indifferent fixed point at the
origin and its multiplier satisfies the Tortrat condition, which
is a generalization of the Cremer condition, of degree three. Then
a cubic perturbation of $f$ is non-linearizable at the origin if
this perturbation is large enough.
submission: September 17, 1999
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