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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 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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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03504688
Contributor : Loïc Jean Dit Teyssier Connect in order to contact the contributor
Submitted on : Wednesday, December 29, 2021 - 4:21:02 PM
Last modification on : Tuesday, January 4, 2022 - 6:23:19 AM

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saddle-loop_rigidity.pdf
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  • HAL Id : hal-03504688, version 1
  • ARXIV : 2112.15058

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Citation

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

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