ИСТИНА

The talk is devoted to a special class of vector (or direction) fields, whose equilibrium (singular) points are not isolated, but fill a submanifold of codimension two in the phase space. Similarly, just as frontal mappings are ungeneric in the space of all smooth mappings, so the considered class of vector fields is ungeneric in the whole space of smooth vector fields. However, they stably appear in many problems in analysis, geometry, dynamical systems theory, etc. The main goal of the talk is a brief survey on local normal forms of such vector fields. Also I shall say a few words about the applications, if I have enough time for that.