  Rotation vectors, as defined for homeomorphisms of the torus that are
isotopic to the identity, are generalized to such homeomorphisms of any
complete Riemannian manifold with non-positive sectional curvature. These
generalized rotation vectors are shown to exist for almost every orbit of such
a dynamical system with respect to any invariant measure with compact support.
The concept is then extended to flows and, as an application, it is shown how
non-null rotation vectors can be used to construct a measurable semi-conjugacy
between a given flow and the geodesic flow of a manifold.
