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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2021 Volume 76, Issue 3(459), Pages 13–92 (Mi rm10001)

This article is cited in 4 papers

Analytic moduli for parabolic Dulac germs

P. Mardešićab, M. Resmanb

a Université Bourgogne Franche-Comté, Institut de Mathématiques de Bourgogne, UMR 5584, CNRS, Dijon, France
b University of Zagreb, Faculty of Science, Department of Mathematics, Bijenicka 30, Zagreb, Croatia

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.

Keywords: Dulac germ, analytic invariants, Écalle–Voronin moduli, Gevrey summability, transseries.

UDC: 517.925

MSC: 37C15, 37F75

Received: 07.11.2019

DOI: 10.4213/rm10001


 English version:
Russian Mathematical Surveys, 2021, 76:3, 389–460

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© Steklov Math. Inst. of RAS, 2024