Analytic moduli for parabolic Dulac germs

Analytic moduli for parabolic Dulac germs

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 br...

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Veröffentlicht in:Russian mathematical surveys 2021-06, Vol.76 (3), p.389-460
Hauptverfasser: Mardešić, P., Resman, M.
Format: Artikel
Sprache:eng
Schlagworte:
analytic invariants
Asymptotic series
Dulac germ
Gevrey summability
Isomorphism
Mathematical analysis
Mathematics
transseries
Écalle–Voronin moduli
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Zusammenfassung: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.
ISSN:0036-0279
1468-4829
DOI:10.1070/RM10001