Abstract

Let $X$ be a polynomial vector field. Gram´s Theorem states that any polynomial system of equations in the coefficients of $X$ invariant under the action of the group $GL(2,R)$ can be expressed by a system of equations formed by $GL$-invariants and comitants (covariants) of $X$. A short historical survey concerning methods of constructing such invariant polynomials will be discussed. Some applications of invariants and comitants will be considered. Main attention will be concentrated on the study of the critical points for the class of quadratic systems.