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Realization of analytic moduli for parabolic Dulac germs

Part of:Qualitative theoryComplex dynamical systemsSmooth dynamical systems: general theory

Published online by Cambridge University Press:  18 January 2021

PAVAO MARDEŠIĆOpen the ORCID record for PAVAO MARDEŠIĆ[Opens in a new window] and
MAJA RESMAN
PAVAO MARDEŠIĆ
Affiliation:
Institut de Mathématiques de Bourgogne, UMR 5584, CNRS, Université Bourgogne Franche-Comté, F-21000 Dijon, France
MAJA RESMAN
Affiliation:
University of Zagreb, Faculty of Science, Department of Mathematics, Bijenička 30, 10000 Zagreb, Croatia
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Abstract

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In a previous paper [P. Mardešić and M. Resman. Analytic moduli for parabolic Dulac germs. Russian Math. Surveys, to appear, 2021, arXiv:1910.06129v2.] we determined analytic invariants, that is, moduli of analytic classification, for parabolic generalized Dulac germs. This class contains parabolic Dulac (almost regular) germs, which appear as first-return maps of hyperbolic polycycles. Here we solve the problem of realization of these moduli.

Keywords

almost regular germsanalytic invariantsEcalle–Voronin moduliGevrey expansionsCauchy–Heine integrals

MSC classification

Primary:37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification37F75: Holomorphic foliations and vector fields
Secondary:34C08: Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 1 , January 2022, pp. 195 - 249
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

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