seminar: The dynamics of maps tangent to the identity in $\C2$ and with non- vanishing index

speaker: Laura Molino (Dipartimento di Matematica - Universita' degli Studi di Parma)

abstract: Let $f$ be a germ of holomorphic self-map of $\C2$ at the origin $O$ tangent to the identity, and with $O$ as a non-dicritical isolated fixed point. A parabolic curve for $f$ is a holomorphic $f$-invariant curve, with $O$ on the boundary, attracted by $O$ under the action of $f$. Abate proved that if the characteristic direction $v\in\Pal1(\C)$ has residual index not belonging to $\Q^+$, then there exist parabolic curves for $f$ tangent to $v$. In this talk we prove by a different method and using Hakim's technique that the conclusion still holds just assuming that the residual index is not vanishing (at least when $f$ is regular along $v$).

timetable:
Thu 25 Jan, 16:00 - 17:00, Aula Dini
documents:

molino.pdf

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