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IMCS/Publications/BASM/Issues/BASM n.1 (44), 2004/

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

Authors: E.V. Starus

Abstract

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".

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