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Linearization of complex hyperbolic Dulac germs

Abstract : We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of hyperbolic transseries in [19].
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Submitted on : Friday, May 20, 2022 - 12:10:14 PM
Last modification on : Saturday, May 21, 2022 - 3:52:38 AM

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D. Peran, M. Resman, J.P. Rolin, T. Servi. Linearization of complex hyperbolic Dulac germs. Journal of Mathematical Analysis and Applications, Elsevier, 2022, 508 (1), pp.125833. ⟨10.1016/j.jmaa.2021.125833⟩. ⟨hal-03673980⟩

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