Geodesic
GL(2,R)-orbits of the polynomial sistems of differential equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2004), pp. 25-40.

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In this work we study the orbits of the polynomial systems x˙=P(x1,x2), x˙=Q(x1,x2) by the action of the group of linear transformations GL(2,R). It is shown that there are not polynomial systems with the dimension of GL-orbits equal to one and there exist GL-orbits of the dimension zero only for linear systems. On the basis of the dimension of GL-orbits the classification of polynomial systems with a singular point O(0,0) with real and distinct eigenvalues is obtained. It is proved that on GL-orbits of the dimension less than four these systems are Darboux integrable. 
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Angela Păşcanu; Alexandru Şubă. $GL(2,R)$-orbits of the polynomial sistems of differential equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2004), pp. 25-40. https://geodesic-test.mathdoc.fr/item/BASM_2004_3_a3/

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