Realization of analytic moduli for parabolic Dulac germs

TL;DR

This paper addresses the realization problem for analytic moduli of parabolic Dulac germs, extending the understanding of their classification and providing methods to construct germs with prescribed invariants.

Contribution

It solves the realization problem for the analytic invariants of parabolic Dulac germs, advancing the classification theory of these dynamical systems.

Findings

Established methods for realizing prescribed moduli.

Extended classification framework for parabolic Dulac germs.

Connected moduli to geometric structures of germs.

Abstract

In a previous paper we have determined analytic invariants, that is, moduli of analytic classification, for parabolic generalized Dulac germs. This class contains parabolic Dulac (almost regular) germs, that appear as first return maps of hyperbolic polycycles. Here we solve the problem of realization of these moduli.