Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
We consider a C∞ family of planar vector fields {Xµˆ}µˆ∈Wˆ having a hyperbolic saddle and we study the Dulac map D(s; ˆµ) and the Dulac time T(s; ˆµ) from a transverse section at the stable separatrix to a transverse section at the unstable separatrix, both at arbitrary distance from the saddle. Sin...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:292711 |
| Acceso en línea: | https://ddd.uab.cat/record/292711 https://dx.doi.org/urn:doi:10.1016/j.jde.2024.05.037 |
| Access Level: | acceso abierto |
| Palabra clave: | Dulac map Dulac time Asymptotic expansion Incomplete Mellin transform |
| Sumario: | We consider a C∞ family of planar vector fields {Xµˆ}µˆ∈Wˆ having a hyperbolic saddle and we study the Dulac map D(s; ˆµ) and the Dulac time T(s; ˆµ) from a transverse section at the stable separatrix to a transverse section at the unstable separatrix, both at arbitrary distance from the saddle. Since the hyperbolicity ratio λ of the saddle plays an important role, we treat it as an independent parameter, so that µˆ = (λ, µ) ∈ Wˆ = (0, +∞) × W, where W is an open subset of R N . For each µˆ0 ∈ Wˆ and L. |
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