Geodesic
The $GL(2,\mathbb R)$-orbits of the homogeneous polynomial differential systems
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2008), pp. 44-56

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In this work, we study the generic homogeneous polynomial differential system $\dot{x}_1= P_k(x_1, x_2)$, $\dot{x}_2=Q_k(x_1,x_2)$ under the action of the center-affine group of transformations of the phase space, $GL(2,\mathbb R)$. We show that if the dimension of the $GL(2,\mathbb R)$-orbits of this system is smaller than four, then $deg(GCD(P_k,Q_k))\geq k-1$. 
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     title = {The $GL(2,\mathbb R)$-orbits of the homogeneous polynomial differential systems},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {44--56},
     publisher = {mathdoc},
     number = {3},
     year = {2008},
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Driss Boularas; Angela Matei; A. Şubă. The $GL(2,\mathbb R)$-orbits of the homogeneous polynomial differential systems. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2008), pp. 44-56. http://geodesic.mathdoc.fr/item/BASM_2008_3_a4/