This article is cited 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.

MSC: 34C14, 34C05, 58F14

Received: 31.12.2002

Language: English

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