The resurgent character of the Fatou coordinates of a simple parabolic germ

Artem Dudko (1) , David Sauzin (2)

1 SBU - Stony Brook University [SUNY]
2 Laboratoire Fibonacci

Given a holomorphic germ at the origin of C with a simple parabolic fixed point, the local dynamics is classically described by means of pairs of attracting and repelling Fatou coordinates and the corresponding pairs of horn maps, of crucial importance for Écalle-Voronin's classification result and the definition of the parabolic renormalization operator. We revisit Écalle's approach to the construction of Fatou coordinates, which relies on Borel-Laplace summation, and give an original and self-contained proof of their resurgent character.

Mots clés: Complex dynamics; Ecalle-Voronin invariants; Resurgent functions

Domaines: Systèmes dynamiques [math.DS]

Artem Dudko, David Sauzin. The resurgent character of the Fatou coordinates of a simple parabolic germ. Comptes Rendus. Mathématique, 2014, 352 (3), pp.255--261. ⟨10.1016/j.crma.2013.12.005⟩. ⟨hal-00849398v3⟩