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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, Number 3, Pages 58–70
(Mi basm207)
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This article is cited in 3 scientific papers (total in 3 papers)
Research articles
Invariant conditions for the dimensions of the $GL(2,R)$-orbits for one differential cubic system
E. V. Starus Institute of Mathematics and Computer Science, Chişinău, Moldova
Abstract:
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.
Keywords and phrases:
Differential system, invariant, comitants, orbit's dimensions invariant sets.
Received: 22.07.2003
Citation:
E. V. Starus, “Invariant conditions for the dimensions of the $GL(2,R)$-orbits for one differential cubic system”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 3, 58–70
Linking options:
https://www.mathnet.ru/eng/basm207 https://www.mathnet.ru/eng/basm/y2003/i3/p58
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Abstract page: | 107 | Full-text PDF : | 38 | References: | 20 | First page: | 1 |
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