Stability of critical points for vector valued functions and Pareto efficiency

In this work we consider the critical points of a vector-valued function f. We study their stability in order to obtain a necessary condition for Paret efficiency. We point out, by an example, that the classical notions of stability (concerning a single point) are not suitable in the settings. We use a stability notion for sets to prove that the counterimage of a minimal point for f is stable.This result is based on the study of a dynamical system defined by a differential inclusion. In the vector case this inclusion plays the same role as gradient system in the scalar setting.