Geodesic
The classification of $GL(2,R)$-orbits' dimensions for system $s(0,2)$ and the factorsystem $s(0,1,2)/GL(2,R)$
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2004), pp. 120-123 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Two-dimensional systems of two autonomous polynomial differential equations with homogeneities of the zero, first and second orders are considered with respect to the group of center-affine transformations $GL(2,R)$. The problem of the classification of $GL(2,R)$-orbits' dimensions is solved completely for system $s(0,2)$ with the help of Lie algebra of operators corresponding to $GL(2,R)$ group, and algebras of invariants and comitants. A factorsystem $s(0,1,2)/GL(2,R)$ for system $s(0,1,2)$ is built and with its help two invariant $GL(2,R)$-integrals are obtained for the system $s(1,2)$ in some necessary conditions for the existence of singular point of the type “center”. 
@article{BASM_2004_1_a13,
     author = {E. V. Starus},
     title = {The classification of $GL(2,R)$-orbits' dimensions for system $s(0,2)$ and the factorsystem $s(0,1,2)/GL(2,R)$},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {120--123},
     year = {2004},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2004_1_a13/}
}
TY  - JOUR
AU  - E. V. Starus
TI  - The classification of $GL(2,R)$-orbits' dimensions for system $s(0,2)$ and the factorsystem $s(0,1,2)/GL(2,R)$
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2004
SP  - 120
EP  - 123
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASM_2004_1_a13/
LA  - en
ID  - BASM_2004_1_a13
ER  - 
%0 Journal Article
%A E. V. Starus
%T The classification of $GL(2,R)$-orbits' dimensions for system $s(0,2)$ and the factorsystem $s(0,1,2)/GL(2,R)$
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2004
%P 120-123
%N 1
%U http://geodesic.mathdoc.fr/item/BASM_2004_1_a13/
%G en
%F BASM_2004_1_a13
E. V. Starus. The classification of $GL(2,R)$-orbits' dimensions for system $s(0,2)$ and the factorsystem $s(0,1,2)/GL(2,R)$. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2004), pp. 120-123. http://geodesic.mathdoc.fr/item/BASM_2004_1_a13/

[1] Boularas D., Calin Iu. F., Timochouk L. A., Vulpe N. I., $T$-comitants of quadratic systems: a study via the translation invariants, Report 96-90, University of Technology, Delft, The Netherlands, 1996

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

[3] Starus E. V., “Invariant conditions for the dimensions of the $GL(2,R)$-orbits for one differential cubic system”, Buletinul Academiei de S̆tiint̆e a Republicii Moldova, Matematica, 2003, no. 3(43), 58–70 | MR

[4] Ovsyannikov L. V., Group analysis of the differential equations, Nauka, Moscow, 1978 (in Russian) ; 1982 (in English) | MR

[5] Sibirsky K. S., Lunkevichi V. A., “Integrals of common quadratic differential system in the centers' cases”, Differential Equations, 18:5 (1982), 786–792 (In Russian) | MR

[6] Sibirsky K. S., Introduction to the Algebraic Theory of Invariants of Differential Equations, Shtiintsa, Kishinev, 1982 (in Russian) ; 1988 (in English) | MR | Zbl