engleski

Classifications of Dulac germs

We consider one-dimensional germs which admit asymptotic expansion inpower-logarithmic scale (the Dulac maps). We discuss formal and analytic classi-fication of such maps, related to the question of formal and analytic embeddingas a time-one map in a vector field. As a crucial step, we construct a (sectorialand formal) Fatou coordinate of a Dulac germ. The research of such germs ismotivated by the question of cyclicity for hyperbolic polycycles in planar vectorfields.This is a joint work with P. Mardešić, J.P. Rolin, and V.Županović.

Dulac germs, analytic classification, Ecalle-Vorionin moduli

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