Geodesic
On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 69-86 
Iurie Calin. On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 69-86. http://geodesic.mathdoc.fr/item/BASM_2003_2_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The linear transformations of autonomous planar polynomial systems of differential equations which reduce these systems to the canonical forms with coefficients expressed as rational functions of $GL(2,\mathbb{R})$-comitants and $GL(2,\mathbb{R})$-invariants are established. Such canonical forms for general quadratic and cubic systems are constructed in concrete forms. Using constructed canonical forms for polynomial systems some rational bases of $GL(2,\mathbb{R})$-comitants depending on the coordinates of one vector are obtained.

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