Realization of analytic moduli for parabolic Dulac germs

Pavao Mardešić (1) , Maja Resman (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 University of Zagreb

In a previous paper [P. Mardešić and M. Resman. Analytic moduli for parabolic Dulac germs. Russian Math. Surveys , to appear, 2021, arXiv:1910.06129v2.] we determined analytic invariants, that is, moduli of analytic classification, for parabolic generalized Dulac germs. This class contains parabolic Dulac (almost regular) germs, which appear as first-return maps of hyperbolic polycycles. Here we solve the problem of realization of these moduli.

Mots clés: almost regular germs; analytic invariants; Ecalle–Voronin moduli; Gevrey expansions; Cauchy–Heine integrals

Domaines: Mathématiques [math]

Pavao Mardešić, Maja Resman. Realization of analytic moduli for parabolic Dulac germs. Ergodic Theory and Dynamical Systems, 2022, 42 (1), pp.195 - 249. ⟨10.1017/etds.2020.139⟩. ⟨hal-03280552⟩