Flow invariant subsets for geodesic flows of manifolds with non-positive curvature
نویسنده
چکیده
Consider a closed, smooth manifold M of non-positive curvature. Write p:UM→M for the unit tangent bundle over M and let � > denote the subset consisting of all vectors of higher rank. This subset is closed and invariant under the geodesic flow � on UM. We define the structured dimension s-dim � > which, essentially, is the dimension of the set p(� > ) of base points of � > . The main result of this paper holds for manifolds with s-dim � > 0, there is an �-dense, flow invariant, closed subset Ξ � �UM�� > such that p(Ξ � )=M. DOI: https://doi.org/10.1017/S0143385704000197 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-21817 Originally published at: Reinold, B (2004). Flow invariant subsets for geodesic flows of manifolds with non-positive curvature. Ergodic Theory and Dynamical Systems, 24(6):1981-1990. DOI: https://doi.org/10.1017/S0143385704000197
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