Generalized Solutions to Degenerate Dynamical Systems
Résumé
The solutions to Degenerate Dynamical Systems of the form A(x) ẋ = f (x) are studied by considering the equation as a dierential inclusion. The set Z = {det(A(x)) = 0}, called the singular set, is assumed to have empty interior. The reasons leading us to the denition of the sets used for the dierential inclusion are exposed in detail. This denition is then applied on the one hand to generic cases, and on the other hand to the particular cases resulting from physics which can be found in [18]. It is shown that generalized solutions may enter, leave, or remain in the singular locus.
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