The theory of singularities of smooth functions defined on finite-dimensional manifolds in particular deals with the analysis of the behavior of smooth functions near critical points belonging to the boundary of the manifold. The analysis of boundary singularities was developed by Arnol'd, Vasil'ev, Davydov, Matov (see [8, 55, 56, 105, 178-180]), Wall (see [185]), Siersma (see [158]), Pitt, Poston, Stewart (see [126]), and others. In particular, Arnol'd proposed to identify boundary singularities with singularities invariant with respect to the operation of elementary involution (an involution is called elementary if the codimension of its mirror is equal to one). Using this principle, he extended the notion of boundary singularity to the complex case and developed the corresponding theory (see [8]). 5387-5323 5387-5423
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