By V.I. Arnol'd, J.S. Joel, V.V. Goryunov, O.V. Lyashko, V.A. Vasil'ev

In the 1st quantity of this survey (Arnol'd et al. (1988), hereafter brought up as "EMS 6") we familiar the reader with the fundamental options and strategies of the idea of singularities of delicate mappings and capabilities. This idea has a number of purposes in arithmetic and physics; the following we start describing those applica tions. however the current quantity is largely self sustaining of the 1st one: the entire techniques of singularity thought that we use are brought throughout the presentation, and references to EMS 6 are constrained to the quotation of technical effects. even supposing our major target is the presentation of analready formulated conception, the readerwill additionally encounter a few relatively fresh effects, it appears unknown even to experts. We pointout a few of these effects. 2 three within the attention of mappings from C into C in§ three. 6 of bankruptcy 1, we outline the bifurcation diagram of this sort of mapping, formulate a K(n, 1)-theorem for the enhances to the bifurcation diagrams of straightforward singularities, provide the definition of the Mond invariant N within the spirit of "hunting for invariants", and we draw the reader's cognizance to a mode of making similar to a mapping from the corresponding functionality on a manifold with boundary. In§ four. 6 of a similar bankruptcy we introduce the idea that of a versal deformation of a functionality with a nonisolated singularity within the dass of capabilities whose severe units are arbitrary whole intersections of mounted dimension.