Quadratic systems with a rational first integral of degree three : A complete classification in the coefficient space ℝ12
Artés Ferragud, Joan Carles ![Identificador ORCID](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume ![Identificador ORCID](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
Fecha: |
2010 |
Resumen: |
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. |
Ayudas: |
Ministerio de Educación y Ciencia MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2001/SGR-00173
|
Derechos: |
Tots els drets reservats. ![](/img/licenses/InC.ico) |
Lengua: |
Anglès |
Documento: |
Article ; recerca ; Versió acceptada per publicar |
Materia: |
Quadratic vector fields ;
Integrability ;
Rational first integral ;
Phase portraits |
Publicado en: |
Rendiconti del Circolo Matematico di Palermo, Vol. 59, Issue 3 (December 2010) , p. 419-449, ISSN 1973-4409 |
DOI: 10.1007/s12215-010-0032-0
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