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Rigidity of saddle loops

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Abstract

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.
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hal-03504688 , version 1 (29-12-2021)

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