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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (43), 2003/

Invariant conditions for the dimensions of the GL(2,R)-orbits for one differential cubic system. (English)

Authors: E.V. Starus

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.

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