%0 Journal Article
%T Rotation Vectors for Homeomorphisms of Non-Positively Curved Manifolds
%A Pablo Lessa
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/1001.0053v4