The GL(2, R)−orbits of the homogeneous polynomial differential systems
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2018-09-02 19:42
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BOULARAS, Driss; MATEI, Angela. The GL(2, R)−orbits of the homogeneous polynomial differential systems. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2008, nr. 3(58), pp. 44-56. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 3(58) / 2008 / ISSN 1024-7696

The GL(2, R)−orbits of the homogeneous polynomial differential systems

Pag. 44-56

Boularas Driss, Matei Angela
 
Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova
 
Disponibil în IBN: 7 decembrie 2013


Rezumat

In this work, we study the generic homogeneous polynomial differential system x˙ 1 = Pk(x1, x2), x˙ 2 = Qk(x1, x2) under the action of the center-affine group of transformations of the phase space, GL(2, R). We show that if the dimension of the GL(2, R)− orbits of this system is smaller than four, then deg(GCD(Pk, Qk)) ≥ k−1.

Cuvinte-cheie
Group action, group orbits, dimension of orbits.