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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (79), 2015/

Rational bases of GL(2, R)-comitants and of GL(2, R)-invariants for the planar system of differential equations with nonlinearities of the fourth degree

Authors: Ciubotaru Stanislav

Abstract

This paper is devoted to the construction of minimal rational bases of $GL(2,\mathbb{R})$-comitants and minimal rational bases of $GL(2, \mathbb{R})$-invariants for the bidimensional system of differential equations with nonlinearities of the fourth degree. For this system, three minimal rational bases of $GL(2, \mathbb{R})$-comitants and two minimal rational bases of $GL(2, \mathbb{R})$-invariants were constructed. It was established that any minimal rational basis of $GL(2,\mathbb{R})$-comitants contains 13 comitants and each minimal rational basis of $GL(2, \mathbb{R})$-invariants contains 11 invariants.

Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
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