A quadratic polynomial differential system can be identified with a single point of ℝ 12 through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of ℝ 12 having a rational first integral of degree 2. We show that there are only 24 topologically different 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 a unique representative of every class modulo an affine change of variables and a rescalling of the time variable. Moreover, each one of these 24 representatives is determined by a set of invariant conditions and each respective first integral is given in invariant form directly in ℝ 12. © 2007 Springer.
|Journal||Rendiconti del Circolo Matematico di Palermo|
|Publication status||Published - 1 Oct 2007|