Geodesic
Invariant conditions for the dimensions of the $GL(2,R)$-orbits for one differential cubic system
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 58-70

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A two-dimensional system of two autonomous polynomial equations with homogeneities of the zero and third orders is considered concerning to the group of center-affine transformations $GL(2,R)$. The problem of the classification of $GL(2,R)$-orbit's dimensions is solved completely for the given system with the help of Lie algebra of operators corresponding to the $GL(2,R)$ group, and algebra of invariants and comitants for the indicated system is built. The theorem on invariant division of all coefficient's set of the considered system to nonintersecting $GL(2,R)$-invariant sets is obtained. 
@article{BASM_2003_3_a5,
     author = {E. V. Starus},
     title = {Invariant conditions for the dimensions of the $GL(2,R)$-orbits for one differential cubic system},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {58--70},
     publisher = {mathdoc},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2003_3_a5/}
}
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E. V. Starus. Invariant conditions for the dimensions of the $GL(2,R)$-orbits for one differential cubic system. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 58-70. http://geodesic.mathdoc.fr/item/BASM_2003_3_a5/