Phase portraits of uniform isochronous centers with homogeneous nonlinearities
We classify the phase portraits in the Poincaré disc of the differential equations of the form x' = - y + xf(x, y), ẏ = x + yf(x, y) where f(x,y) is a homogeneous polynomial of degree n - 1 when n = 2, 3, 4, 5, and f has only simple zeroes. We also provide some general results on these uniform...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:239791 |
| Acceso en línea: | https://ddd.uab.cat/record/239791 https://dx.doi.org/urn:doi:10.1007/s10883-021-09529-2 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomial vector field Uniform isochronous center Phase portrait Poincaré disc |
| Sumario: | We classify the phase portraits in the Poincaré disc of the differential equations of the form x' = - y + xf(x, y), ẏ = x + yf(x, y) where f(x,y) is a homogeneous polynomial of degree n - 1 when n = 2, 3, 4, 5, and f has only simple zeroes. We also provide some general results on these uniform isochronous centers for all n ≥ 2. All our results have been revised by the program P4; see Chaps. 9 and 10 of Dumortier et al. (UniversiText, Springer-Verlag, New York, 2006). |
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