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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, Number 2, Pages 69–86
(Mi basm199)
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This article is cited in 13 scientific papers (total in 13 papers)
Research articles
On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations
Iurie Calin Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Republic of Moldova
Abstract:
The linear transformations of autonomous planar polynomial systems of differential equations which reduce these systems to the canonical forms with coefficients expressed as rational functions of $GL(2,\mathbb{R})$-comitants and $GL(2,\mathbb{R})$-invariants are established. Such canonical forms for general quadratic and cubic systems are constructed in concrete forms. Using constructed canonical forms for polynomial systems some rational bases of $GL(2,\mathbb{R})$-comitants depending on the coordinates of one vector are obtained.
Keywords and phrases:
differential system, comitant, invariant, transformation, canonical form, rational basis.
Received: 31.12.2002
Citation:
Iurie Calin, “On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 2, 69–86
Linking options:
https://www.mathnet.ru/eng/basm199 https://www.mathnet.ru/eng/basm/y2003/i2/p69
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Abstract page: | 366 | Full-text PDF : | 100 | References: | 38 | First page: | 1 |
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