Abstract
A quadratic polynomial differential system can be identified with a single point of\(\mathbb{R}^{12} \) through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of\(\mathbb{R}^{12} \) 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\(\mathbb{R}^{12} \)
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The authors are partially supported by a MEC/FEDER grant MTM2005-06098-C02-01, and a CONACIT grant number 2005SGR-00550.
Partially supported by CRDF-MRDA CERIM-1006-06
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Artés, J.C., Llibre, J. & Vulpe, N. Quadratic systems with a rational first integral of degree 2: A complete classification in the coefficient space\(\mathbb{R}^{12} \) . Rend. Circ. Mat. Palermo 56, 417–444 (2007). https://doi.org/10.1007/BF03032094
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DOI: https://doi.org/10.1007/BF03032094