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A GL(2,R)-orbits of the polynomial sistems of differential equations. (English)
Authors: Angela Pascanu, Şubă Alexandru
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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
E-mail:
Department of Mathematics,
State University of Tiraspol MD-2069,
Chisinau, Moldova
Alexandru Subu
Department of Mathematics,
State University of Moldova MD-2009,
Chisinau, Moldova
E-mail:
Fulltext
– 0.18 Mb
Contents
- Exponential inflationary economic growth. (English)
- The optimal flow in dynamic networks with nonlinear cost functions on edges. (English)
- On check character systems over groups. (English)
- A GL(2,R)-orbits of the polynomial sistems of differential equations. (English)
- Asymptotic Stability of autonomous and Non-Autonomous Discrete Linear Inclusions. (English)
- Stability and fold bifurcation in a system of two coupled demand-supply models. (English)
- Some hyperbolic manifolds. (English)
- Variety of the center and limit cycles of a cubic system, which is reduced to Lienard form. (English)
- Modeling and optimization of melting and solidification process. (English)
