The classification of GL(2,R)-orbits’ dimensions for system s(0, 2) and the factorsystem s(0, 1, 2)/GL(2,R)

Staruş Elena

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2023-12-18 08:38

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STARUŞ, Elena. The classification of GL(2,R)-orbits’ dimensions for system s(0, 2) and the factorsystem s(0, 1, 2)/GL(2,R). In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2004, nr. 1(44), pp. 120-123. ISSN 1024-7696.

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 1(44) / 2004 / ISSN 1024-7696 /ISSNe 2587-4322

The classification of GL(2,R)-orbits’ dimensions for system s(0, 2) and the factorsystem s(0, 1, 2)/GL(2,R)

Pag. 120-123

Staruş Elena

Institute of Mathematics and Computer Science ASM

Disponibil în IBN: 7 decembrie 2013

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Rezumat

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 al- gebras 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”.

Cuvinte-cheie
differential system,

GL(2, R)-orbit, factorsystem, invariant integral.

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