Klymenko O. Deformation of systems of forms and mappings.

We construct an algorithm that reduces each matrix in an neighborhood of J to Arnold's normal form by smooth similarity transformations and calculates the transforming matrix. We give block-triangular normal forms of matrices with respect to smooth transformations of similarity and block-triangular normal forms of matrix pencils with respect to smooth equivalence transformations. The closure graphs for congruence classes of 2x2 and 3x3 matrices are constructed. We give a new defnition of bundles. The closure graphs of such bundles for 2x2 and 3x3 matrices are constructed. The closure graph for *congruence classes of 2x2 is constructed.