STABILITY OF CRITICAL POINTS OF QUADRATIC HOMOGENEOUS DYNAMICAL SYSTEMS

In this work, we give sufficient conditions ensuring the instability of a critical point of a homogeneous quadratic system in R-n using the multiplication of the corresponding non-associative algebra. This result generalizes a theorem of Zalar and Mencinger (see [5]). We also state a classification theorem giving the stability or the instability of any stationary point of a quadratic homogeneous system in R-2. As expected, the second theorem in [5] is part of this classification.