Analytic moduli for parabolic Dulac germs

Abstract

This paper gives moduli of analytic classification for parabolic Dulac germs (that is, almost regular germs). Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of Écalle–Voronin-type germs of analytic diffeomorphisms. The result is stated in a broader class of parabolic generalized Dulac germs having power- logarithmic asymptotic expansions. Bibliography: 23 titles.