Geodesic
The $GL(2,{\mathbb R})$-orbits of polynomial differential systems of degree four
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 65-72 
Angela Păşcanu. The $GL(2,{\mathbb R})$-orbits of polynomial differential systems of degree four. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 65-72. http://geodesic.mathdoc.fr/item/BASM_2006_3_a6/
@article{BASM_2006_3_a6,
     author = {Angela P\u{a}\c{s}canu},
     title = {The $GL(2,{\mathbb R})$-orbits of polynomial differential systems of degree four},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {65--72},
     year = {2006},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2006_3_a6/}
}
TY  - JOUR
AU  - Angela Păşcanu
TI  - The $GL(2,{\mathbb R})$-orbits of polynomial differential systems of degree four
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2006
SP  - 65
EP  - 72
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/BASM_2006_3_a6/
LA  - en
ID  - BASM_2006_3_a6
ER  - 
%0 Journal Article
%A Angela Păşcanu
%T The $GL(2,{\mathbb R})$-orbits of polynomial differential systems of degree four
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2006
%P 65-72
%N 3
%U http://geodesic.mathdoc.fr/item/BASM_2006_3_a6/
%G en
%F BASM_2006_3_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we characterize the $GL(2,{\mathbb R})-$orbits of the differential systems $\dot{x}_1=P(x_1,x_2)$, $\dot{x}_2=Q(x_1,x_2),$ where $P,Q$ are polynomials of degree four, with respects to their dimensions.

[1] Academic Press, 1982 | MR | Zbl

[2] Popa M. N., Applications of algebras to differential systems, Academy of Sciences of Moldova, Chişinău, 2001 (in Russian) | Zbl

[3] Braicov A. V., Popa M. N., “The $GL(2,\mathbb R)$-orbits of differential system with homogeneites second order”, The Internationals Conference “Differential and Integral Equations” (Odessa, September 12–14, 2000), 31

[4] Boularas D., Braicov A. V., Popa M. N., “Invariant conditions for dimensions of $GL(2,\mathbb R)$-orbits for quadratic differential system”, Bul. Acad. Sci. Rep. Moldova, Math., 2000, no. 2(33), 31–38 | MR | Zbl

[5] Boularas D., Braicov A. V., Popa M. N., “The $GL(2,\mathbb R)$-orbits of differential system with cubic homogeneites”, Bul. Acad. Sci. Rep. Moldova, Math., 2001, no. 1(35), 81–82 | MR | Zbl

[6] Naidenova E. V., Popa M. N., “On a classification of Orbits for Cubic Differential Systems”, Abstracts of “16th International Symposium on Nonlinear Acoustics”, section “Modern group analysis” (MOGRAN-9) (August 19–23, 2002, Moscow), 274

[7] Naidenova E. V., Popa M. N., “$GL(2,\mathbb R)$-orbits for one cubic system”, Abstracts of “11th Conference on Applied and Industrial Mathematics” (May 29–31, 2003, Oradea, Romania), 57

[8] Starus E. V., “Invariant conditions for the dimensions of the $GL(2,\mathbb R)$-orbits for one differential cubic system”, Bul. Acad. Sci. Rep. Moldova, Math., 2003, no. 3(43), 58–70 | MR

[9] Starus E. V., “The classification of the $GL(2,\mathbb R$-orbit's dimensions for the system $s(0,2)$ and a factorsystem $s(0,1,2)/GL(2,\mathbb R)$”, Bul. Acad. Sci. Rep. Moldova, Math., 2004, no. 1(44), 120–123 | MR | Zbl

[10] Păşcanu A., Şubă A., “$GL(2,\mathbb R)$-orbits of the polynomial systems of differential equation”, Bul. Acad. Sci. Rep. Moldova, Math., 2004, no. 3(46), 25–40