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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, Number 3, Pages 44–56 (Mi basm35)  

Research articles

The $GL(2,\mathbb R)$-orbits of the homogeneous polynomial differential systems

Driss Boularasa, Angela Mateib, A. Şubăc

a Département de Mathématiques, Université de Limoges
b Department of Mathematics, State University of Tiraspol, Chişinău, Moldova
c Department of Mathematics, State University of Moldova, Chişinău, Moldova

Abstract: In this work, we study the generic homogeneous polynomial differential system $\dot{x}_1= P_k(x_1, x_2)$, $\dot{x}_2=Q_k(x_1,x_2)$ under the action of the center-affine group of transformations of the phase space, $GL(2,\mathbb R)$. We show that if the dimension of the $GL(2,\mathbb R)$-orbits of this system is smaller than four, then $deg(GCD(P_k,Q_k))\geq k-1$.

Keywords and phrases: Group action, group orbits, dimension of orbits.

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Bibliographic databases:

MSC: 34C05, 34C14
Language: English

Citation: Driss Boularas, Angela Matei, A. Şubă, “The $GL(2,\mathbb R)$-orbits of the homogeneous polynomial differential systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, no. 3, 44–56

Citation in format AMSBIB
\Bibitem{BouMatUba08}
\by Driss~Boularas, Angela~Matei, A.~\c Sub{\u a}
\paper The $GL(2,\mathbb R)$-orbits of the homogeneous polynomial differential systems
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2008
\issue 3
\pages 44--56
\mathnet{http://mi.mathnet.ru/basm35}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2478713}
\zmath{https://zbmath.org/?q=an:1173.34023}


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