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...
| Autor: | |
|---|---|
| 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 |
| 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. |
|---|