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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (60), 2009/

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

Authors: Gherştega Natalia, Orlov Victor, Vulpe Nicolae

Abstract

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.

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