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Rigidity of saddle loops (2112.15058v1)
Published 30 Dec 2021 in math.DS
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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