The Fatou coordinate for parabolic Dulac germs

Pavao Mardešić (1) , Maja Resman (2) , Jean-Philippe Rolin (1) , Vesna Županović (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Department of Mathematics [Zagreb]
3 Department of Applied Mathematics [Zagreb]

We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated logarithm monomials.

Mots clés: orbits; classification; diffeomorphisms; normal forms; epsilon-neighborhoods; Transseries; Asymptotic expansion; Fatou coordinate; Embedding in a flow; Dulac germ

Domaines: Systèmes dynamiques [math.DS]

Pavao Mardešić, Maja Resman, Jean-Philippe Rolin, Vesna Županović. The Fatou coordinate for parabolic Dulac germs. Journal of Differential Equations, 2019, 266 (6), pp.3479-3513. ⟨10.1016/j.jde.2018.09.008⟩. ⟨hal-01962092⟩