engleski

Classifications of Dulac maps and epsilon-neighborhoods

We give formal classification results for parabolic Dulac germs in the class of power-logarithm transseries. Parabolic Dulac germs appear as first-return maps around hyperbolic polycycles, and admit a power-logarithm asymptotic expansion. We further construct a Fatou coordinate for a parabolic Dulac germ (formal and sectorially analytic). We describe one application: reading the formal class of a germ from the initial part of the asymptotic expansion of the length of the epsilon-neighborhood of one orbit.This is a joint work with Pavao Mardeöic, Jean-Philippe Rolin and Vesna Županovic.

Dulac maps, normal forms, epsilon-neighborhoods

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