Fake saddles and their transition maps

We study degenerate singular points of planar vector fields inside a (degenerate) flow box. These kind of singularities are called fake saddles and their linear parts are always zero. We characterize fake saddles with non-zero second-order jet and we give the first term of a uniform asymptotic expan...

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Detalles Bibliográficos
Autor: Marín, David|||0000-0003-4422-6418
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:dnet:uabarcelona_::aee0b9988656dcf2de54f58fe6343399
Acceso en línea:https://ddd.uab.cat/record/327411
https://dx.doi.org/urn:doi:10.14232/ejqtde.2026.1.5
Access Level:acceso abierto
Palabra clave:Singularities
Poincaré and Dulac transition maps
Asymptotic expansion
Uniform flatness
Stability
Descripción
Sumario:We study degenerate singular points of planar vector fields inside a (degenerate) flow box. These kind of singularities are called fake saddles and their linear parts are always zero. We characterize fake saddles with non-zero second-order jet and we give the first term of a uniform asymptotic expansion of the Poincaré map between two transverse sections to their corresponding singular fiber, determining its stability.