The Easiest Polynomial Differential Systems in ℝ 3 Having an Invariant Hyperboloid
This paper answers the following two questions: What are the easiest polynomial differential systems in ℝ3 having an invariant hyperboloid of one sheet, or an invariant hyperboloid of two sheets? And, for this kind of polynomial differential systems, what are their phase portraits on such an invaria...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:326013 |
| Acceso en línea: | https://ddd.uab.cat/record/326013 https://dx.doi.org/urn:doi:10.1142/S0218127425501391 |
| Access Level: | acceso embargado |
| Palabra clave: | Polynomial differential system in R3 Invariant hyperboloid Phase portrait |
| Sumario: | This paper answers the following two questions: What are the easiest polynomial differential systems in ℝ3 having an invariant hyperboloid of one sheet, or an invariant hyperboloid of two sheets? And, for this kind of polynomial differential systems, what are their phase portraits on such an invariant hyperboloids? To solve these questions, a method based on first integrals, symmetry, analysis of the nature of equilibrium points, and invariant algebraic surfaces is employed. |
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