ИСТИНА

The talk is devoted to singularities of geodesic flows on 2-dimensional manifolds equipped with signature varying metrics (often called pseudo-Riemannian). Generically, such a manifold consists of a number of domains where the signature of metric is constant, and a number of curves where the metric degenerates. Degenerate points of the metric are singular points of the corresponding geodesic flow, and the behavior of geodesics at such points differs from Riemannian geometry. Generically, geodesics cannot pass through a degenerate point in arbitrary tangential directions, but only in some admissible directions that correspond to real roots of a cubic polynomial; and almost all geodesics at a degenerate point have cusp. In this talk, we consider the behavior of geodesics at generic degenerate points in detail.