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