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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2008, номер 3, страницы 44–56
(Mi basm35)
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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
Аннотация:
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 $deg(GCD(P_k,Q_k))\geq k-1$.
Ключевые слова и фразы:
Group action, group orbits, dimension of orbits.
Образец цитирования:
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm35 https://www.mathnet.ru/rus/basm/y2008/i3/p44
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