Author： Lessa Pablo
Publisher： IOP Publishing
ISSN： 0951-7715
Source： Nonlinearity, Vol.24, Iss.11, 2011-11, pp. : 3237-3266
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Abstract
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.
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