Geodesic Flows on Closed Riemannian Manifolds Without Focal Points

In this paper it is proved that a geodesic flow on a two-dimensional compact manifold of genus greater than 1 with Riemannian metric without focal points is isomorphic with a Bernoulli flow. This result generalizes to the multidimensional case. The proof is based on establishing some metric properties of flows with nonzero Ljapunov exponents (the K-property, etc.), and also the construction of horospheres and leaves on a very wide class of Riemannian manifolds, together with a study of some of their geometric properties.Bibliography: 24 titles.