Abstract. 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.
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