Geodesic
On rational bases of GL(2,R)-comitants of planar polynomial systems of differential equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 69-86.

Voir la notice de l'article provenant de la source Math-Net.Ru

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,R)-comitants and GL(2,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,R)-comitants depending on the coordinates of one vector are obtained. 
@article{BASM_2003_2_a6,
     author = {Iurie Calin},
     title = {On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {69--86},
     publisher = {mathdoc},
     number = {2},
     year = {2003},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2003_2_a6/}
}
TY  - JOUR
AU  - Iurie Calin
TI  - On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2003
SP  - 69
EP  - 86
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2003_2_a6/
LA  - en
ID  - BASM_2003_2_a6
ER  - 
%0 Journal Article
%A Iurie Calin
%T On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2003
%P 69-86
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2003_2_a6/
%G en
%F BASM_2003_2_a6
Iurie Calin. On rational bases of $GL(2,\mathbb{R})$-comitants of planar polynomial systems of differential equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 69-86. https://geodesic-test.mathdoc.fr/item/BASM_2003_2_a6/

[1] N. I. Vulpe, Polinomialnye bazisy komitantov differentsialnykh sistem i ikh prilozheniya v kachestvennoi teorii, Shtiintsa, Kishinev, 1986 | MR | Zbl

[2] Sibirsky K. S., Introduction to the Algebraic Theory of Invariants of Differential Equations, Manchester University Press, 1988 | MR | Zbl

[3] Boularas Driss, Iu. Calin, L. Timochouk, N. Vulpe, $T$-comitants of quadratic systems: A study via the translation invariants, Report 96-90, Delft University of Technology, Faculty of Technical Mathematics and Informatics, 1996, p. 1–36.

[4] G. B. Gurevich, Foundations of the Theory of Algebraic Invariants, Noordhoff, Groningen, 1964 | MR | Zbl

[5] J. H. Grace, A. Young, The Algebra of Invariants, Cambridge University Press, 1903 | Zbl

[6] N. I. Vulpe, K. S. Sibirskii, “Affinnaya klassifikatsiya kvadratichnoi sistemy”, Differentsialnye uravneniya, 10:12 (1974), 2111–2124 | MR | Zbl

[7] Bularas Driss, “Usloviya nalichiya osoboi tochki tipa tsentra obschei kvadratichnoi differentsialnoi sistemy”, Dinamicheskie sistemy i uravneniya matematicheskoi fiziki, Shtiintsa, Kishinev, 1988, 32–49 | MR

[8] V. I. Danilyuk, K. S. Sibirskii, “Sizigii mezhdu tsentroaffinnymi invariantami kvadratichnoi differentsialnoi sistemy”, Differentsialnye uravneniya, 17:2 (1981), 210–219 | MR | Zbl

[9] P. M. Makar, M. N. Popa, “Tipicheskoe predstavlenie polinomialnykh differentsialnykh sistem s pomoschyu komitantov pervogo poryadka”, Izvestiya AN RM, Matematika, 1996, no. 3(22), 52–60 | MR | Zbl

[10] Iu. Calin, “About rational bases of comitants of cubic differential system”, First Conference of the Mathematical Sosiety of the Republic of Moldova, Abstracts (Chisinau, August 16–18, 2001), 13–15 | Zbl

[11] Iu. Calin, “Syzygies among comitants of the homogeneous cubic differential system”, First Conference of the Mathematical Sosiety of the Republic of Moldova, Abstracts (Chisinau, August 16–18, 2001), 15–16