Quadratic systems with an integrable saddle: A complete classification in the coefficient space ℝ ¹²

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 an integrable saddle. We show that there are only 47 topologically different phase portraits in the Poincaré disk associated to this family of quadratic systems up to a reversal of the sense of their orbits. Moreover each one of these 47 representatives is determined by a set of affine invariant conditions. © 2012 Elsevier Ltd. All rights reserved.