Rigidity of saddle loops

Daniel Panazzolo (1) , Maja Resman (2) , Loïc Teyssier (3)

1 Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar
2 Department of Mathematics [Zagreb]
3 IRMA - Institut de Recherche Mathématique Avancée

A saddle loop is a germ of a holomorphic foliation near a homoclinic saddle connection. We prove that they are classied by their Poincaré rst-return map. We also prove that they are formally rigid when the Poincaré map is multivalued. Finally, we provide a list of all analytic classes of Liouville-integrable saddle loops.

Domaines: Systèmes dynamiques [math.DS]

Daniel Panazzolo, Maja Resman, Loïc Teyssier. Rigidity of saddle loops. 2021. ⟨hal-03504688⟩