Geodesic
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
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2015), pp. 14-34

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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. 
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     author = {Stanislav Ciubotaru},
     title = {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},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {14--34},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2015_3_a1/}
}
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Stanislav Ciubotaru. 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. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2015), pp. 14-34. http://geodesic.mathdoc.fr/item/BASM_2015_3_a1/