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Russian Mathematical Surveys, 2021, Volume 76, Issue 3, Pages 389–460
DOI: https://doi.org/10.1070/RM10001 (Mi rm10001) 		 
This article is cited in 3 scientific papers (total in 3 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
English version PDF (1131 kB) Citations (3)
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DOI: https://doi.org/10.1070/RM10001
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.
Funding agency Grant number
Croatian Science Foundation UIP-2017-05-1020
PZS-2019-02-3055
Unity Through Knowledge Fund 16
Agence Nationale de la Recherche ANR-17-EURE-0002
This research was supported by the Croatian Unity Through Knowledge Fund (UKF) “My first collaboration grant” (project no. 16), by the Croatian Science Foundation (HRZZ) grants UIP-2017-05-1020 and PZS-2019-02-3055 from “Research Cooperability” funded by the European Social Fund, and by the EIPHI Graduate School (contract ANR-17-EURE-0002). The UKF grant fully supported the 6-month stay of the second author at University of Burgundy in 2018.
Received: 07.11.2019
Russian version:
Uspekhi Matematicheskikh Nauk, 2021, Volume 76, Issue 3(459), Pages 13–92
DOI: https://doi.org/10.4213/rm10001
Bibliographic databases:
Document Type: Article
UDC: 517.925
MSC: 37C15, 37F75
Language: English
Original paper language: Russian
Citation: P. Mardešić, M. Resman, “Analytic moduli for parabolic Dulac germs”, Uspekhi Mat. Nauk, 76:3(459) (2021), 13–92; Russian Math. Surveys, 76:3 (2021), 389–460
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
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