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JOURNALS // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Archive

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015 Number 3, Pages 14–34 (Mi basm404)

This article is cited in 3 papers

Research articles

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

Stanislav Ciubotaru

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

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.

Keywords and phrases: polynomial differential systems, invariant, comitant, transvectant, rational basis.

MSC: 34C05, 58F14

Received: 02.01.2015

Language: English



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