COMPUTATION OF AFFINE COVARIANTS OF BIVARIATE DIFFERENTIAL SYSTEMS

Abstract. This paper deals with affine covariants of autonomous differential systems. We give a constructive method for computing them. This method allows in particular to deduce a (minimal) system of generators of the algebra of affine covariants from one of centro-afffine invariants. In the case of planar quadratic differential systems, we give a minimal system of the algebra of center-affine covariants and using the previous method we construct a minimal system of generators of the algebra of affine covariants. Computations are made with Maple. All algorithms constitute the package SIB. Key words. Nonlinear differential systems, transformations of differentia