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Pàgina inicial > Articles > Articles publicats > Quadratic systems with a rational first integral of degree three : |
Data: | 2010 |
Resum: | 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. |
Ajuts: | Ministerio de Educación y Ciencia MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2001/SGR-00173 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Quadratic vector fields ; Integrability ; Rational first integral ; Phase portraits |
Publicat a: | Rendiconti del Circolo Matematico di Palermo, Vol. 59, Issue 3 (December 2010) , p. 419-449, ISSN 1973-4409 |
Postprint 22 p, 510.1 KB |