1. Analytic moduli for parabolic Dulac germs
- Author
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Pavao Mardešić, Maja Resman, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Croatian Unity Through Knowledge Fund (UKF) 'My first collaboration grant'16Croatian Science Foundation (HRZZ) - European Social FundUIP-2017-05-1020PZS-2019-02-3055EIPHI Graduate SchoolANR-17-EURE-0002UKF grant, and ANR-17-EURE-0002,EIPHI,Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité(2017)
- Subjects
Pure mathematics ,Class (set theory) ,Mathematics::Dynamical Systems ,General Mathematics ,Dulac germ ,Dynamical Systems (math.DS) ,01 natural sciences ,Moduli ,Mathematics::Algebraic Geometry ,0103 physical sciences ,FOS: Mathematics ,Mathematics - Dynamical Systems ,[MATH]Mathematics [math] ,0101 mathematics ,transseries ,Mathematics ,Sequence ,Mathematics::Complex Variables ,010102 general mathematics ,State (functional analysis) ,37C15, 37F75 ,analytic invariants ,Gevrey summability ,Almost regular germ ,Ecalle-Voronin moduli ,ecalle-Voronin moduli ,010307 mathematical physics - Abstract
In this paper we give moduli of analytic classification for parabolic Dulac i.e. almost regular germs. Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of Ecalle-Voronin-like germs of analytic diffeomorphisms. We state the result in a bigger class of parabolic generalized Dulac germs having power-logarithmic asymptotic expansions., 63 pages, 5 figures
- Published
- 2021
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