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IMCS/Publications/BASM/Issues/BASM n.3 (46), 2004/

A GL(2,R)-orbits of the polynomial sistems of differential equations. (English)

Authors: Angela Pascanu, Şubă Alexandru

Abstract

In this work we study the orbits of the polynomial systems x' = P(x1, x2), x' = Q(x1, x2) by the action of the group of linear transformations GL(2,R). It is shown that there are not polynomial systems with the dimension of GL-orbits equal to one and there exist GL-orbits of the dimension zero only for linear systems. On the basis of the dimension of GL-orbits the classification of polynomial systems with a singular point O(0,0) with real and distinct eigenvalues is obtained. It is proved that on GL-orbits of the dimension less than four these systems are Darboux integrable.

Angela Pascanu
Department of Mathematics,
State University of Tiraspol MD-2069,
Chisinau, Moldova
Alexandru Subu
Department of Mathematics,
State University of Moldova MD-2009,
Chisinau, Moldova
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