Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant
Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalf...
| 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:258883 |
| Acceso en línea: | https://ddd.uab.cat/record/258883 |
| Access Level: | acceso abierto |
| Palabra clave: | Quadratic vector fields Algebraic invariant curve Darboux invariant Global phase portrait |
| Sumario: | Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalforms for the quadratic systems in QS3. Working with these normal forms we complete the characterization of the phase portraits in QS3 having a Darboux invariant of the form f(x, y)est, with s ∈ R. |
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