Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2005), pp. 51-64
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Natalia Gherstega; Mihail Popa. Lie algebras of the operators and three-dimensional polynomial differential systems. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2005), pp. 51-64. http://geodesic.mathdoc.fr/item/BASM_2005_2_a2/
@article{BASM_2005_2_a2,
author = {Natalia Gherstega and Mihail Popa},
title = {Lie algebras of the operators and three-dimensional polynomial differential systems},
journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
pages = {51--64},
year = {2005},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BASM_2005_2_a2/}
}
TY - JOUR
AU - Natalia Gherstega
AU - Mihail Popa
TI - Lie algebras of the operators and three-dimensional polynomial differential systems
JO - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY - 2005
SP - 51
EP - 64
IS - 2
UR - http://geodesic.mathdoc.fr/item/BASM_2005_2_a2/
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%0 Journal Article
%A Natalia Gherstega
%A Mihail Popa
%T Lie algebras of the operators and three-dimensional polynomial differential systems
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2005
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%G en
%F BASM_2005_2_a2
The defining equations are built for the representation of continuous groups in the space of variables and coefficients of multi-dimensional polynomial differential systems of the first order. Lie theorem on integrating factor is obtained for three-dimensional polynomial differential systems and the invariant $GL(3,\mathbb{R})$-integrals are constructed for three-dimensional affine differential system.
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[2] Popa M. N., Algebraic methods for differential systems, Seria Matematică Aplicată şi Industrială, 15, Editura the Flower Power, Universitatea din Piteşti, 2004 (in Romanian) | MR | Zbl
[4] Stepanov V. V., Course of differential equations, Moscow, 1950 (in Russian)
[5] Rashevsky P. K., Geometrical theory of partial differential equations, Moscow, 1947 (in Russian)
[6] Gherstega N. N., Popa M. N., “Mixed comitants and $GL(3,R)$-orbit's dimensions for the three-dimensional differential systems”, Buletin Ştiinţific Universitatea din Piteşti, Seria Matematică şi Informatică, 2003, no. 9, 149–154
