Quadratic systems with a rational first integral of degree 2: A complete classification in the coefficient space ℝ 12

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Abstract

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.
Original languageEnglish
Pages (from-to)417-444
JournalRendiconti del Circolo Matematico di Palermo
Volume56
DOIs
Publication statusPublished - 1 Oct 2007

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