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

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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. 
@article{BASM_2003_2_a6,
     author = {Iurie Calin},
     title = {On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {69--86},
     publisher = {mathdoc},
     number = {2},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2003_2_a6/}
}
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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/