Quadratic systems with a rational first integral of degree three
A quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. Here using the algebraic invariant theory, we characterize...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:226092 |
| Acceso en línea: | https://ddd.uab.cat/record/226092 https://dx.doi.org/urn:doi:10.1007/s12215-010-0032-0 |
| Access Level: | acceso abierto |
| Palabra clave: | Quadratic vector fields Integrability Rational first integral Phase portraits |
| Sumario: | A quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. Here using the algebraic invariant theory, we characterize all the non-degenerate quadratic polynomial differential systems in R12 having a rational first integral of degree 3. We show that there are only 31 different topological phase portraits in the Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and a rescaling of the time variable. Moreover, each one of these 31 representatives is determined by a set of algebraic invariant conditions and we provide for it a first integral. |
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