A complete classification of quadratic differential systems according to the dimensions of Aff(2, R)−orbits
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GHERŞTEGA, Natalia; ORLOV, Victor; VULPE, Nicolae. A complete classification of quadratic differential systems according to the dimensions of Aff(2, R)−orbits. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2009, nr. 2(60), pp. 29-54. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 2(60) / 2009 / ISSN 1024-7696

A complete classification of quadratic differential systems according to the dimensions of Aff(2, R)−orbits

Pag. 29-54

Gherştega Natalia, Orlov Victor, Vulpe Nicolae
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 16 decembrie 2013


Rezumat

In this article we consider the action of the group Aff (2, R) of affine transformations and time rescaling on real planar quadratic differential systems. Via affine invariant conditions we give a complete stratification of this family of systems according to the dimension D of affine orbits proving that 3 ≤ D ≤ 6. Moreover we give a complete topological classification of all the systems located on the orbits of dimension D ≤ 5 constructing the affine invariant criteria for the realization of each of 49 possible topologically distinct phase portraits

Cuvinte-cheie
quadratic differential system, Lie algebra of operators, affine invariant polynomial,

Aff (2, R)−orbit