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arXiv · 2112.15058

Rigidity of saddle loops

Daniel Panazzolo·Maja Resman·Loïc Teyssier
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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 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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Daniel Panazzolo, Maja Resman, Loïc Teyssier. 2021-12-30. Rigidity of saddle loops. https://arxiv.org/abs/2112.15058

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