Okuyama, Yusuke

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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