Planar Quadratic Differential Systems with Invariants of the Form ax2 + bxy + cy2 + dx + ey + c1t
A function I (x, y, t) constant on the solutions of a differential system in R2 is called an invariant. We classify all planar quadratic differential systems having invariants of the form I (x, y, t) = ax2 + bxy + cy2 + dx + ey + c1t with c ≠ 0. There are 13 different families of quadratic systems h...
| 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:299738 |
| Acceso en línea: | https://ddd.uab.cat/record/299738 https://dx.doi.org/urn:doi:10.1007/s41980-024-00888-7 |
| Access Level: | acceso abierto |
| Palabra clave: | Planar quadratic differential system Invariant Hamiltonian first integral Poincaré compactification Singular point Chordal quadratic system |
| Sumario: | A function I (x, y, t) constant on the solutions of a differential system in R2 is called an invariant. We classify all planar quadratic differential systems having invariants of the form I (x, y, t) = ax2 + bxy + cy2 + dx + ey + c1t with c ≠ 0. There are 13 different families of quadratic systems having invariants of this form. As far as we know this is the first time that quadratic differential systems having an invariant different from a Darboux invariant have been classified. |
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