Analytic moduli for parabolic Dulac germs

TL;DR

This paper provides a classification framework for parabolic Dulac germs, which are related to hyperbolic polycycles, using a sequence of Ecalle-Voronin-like invariants, extending to a broader class with power-logarithmic asymptotics.

Contribution

It introduces analytic moduli for parabolic Dulac germs, expanding the classification to include generalized germs with power-logarithmic asymptotic expansions.

Findings

Classification of Dulac germs via Ecalle-Voronin-like invariants

Extension to a broader class with asymptotic expansions

Framework for analytic classification of almost regular germs

Abstract

In this paper we give moduli of analytic classification for parabolic Dulac i.e. almost regular germs. Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of Ecalle-Voronin-like germs of analytic diffeomorphisms. We state the result in a bigger class of parabolic generalized Dulac germs having power-logarithmic asymptotic expansions.