On the singularities of differentiable mappings

We discuss the structure of the set of the singularities of differentiable mappings of manifolds. In Morse theory, the non-degenerated singularities of differentiable functions are considered. This theory has a lot of applications to the topology of manifolds. The structure of the set of degenerated singularities is much more complicated. In this field, there are a lot of open problems. Our aim is the study of degenerated singularities defined on the manifold of the solutions of the system of equations. The mappings under considering obey the conditions of non-degeneration of some special Jacobi matrices, whose elements are the partial derivatives of given order. Under some conditions, we prove that the set of singularities has a zero Jordan measure.

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