Linearization of complex hyperbolic Dulac germs

D. Peran (1) , M. Resman (2) , Jean-Philippe Rolin (3) , T. Servi (4)

1 Faculty of Sciences, University of Split
2 University of Zagreb
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]
4 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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].

Mots clés: Dulac germs and series; Hyperbolic fixed point; Linearization; Koenigs' sequence

Domaines: Mathématiques [math]

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