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Flow invariant subsets for geodesic flows of manifolds with non-positive curvature


Reinold, B (2004). Flow invariant subsets for geodesic flows of manifolds with non-positive curvature. Ergodic Theory and Dynamical Systems, 24(6):1981-1990.

Abstract

Consider a closed, smooth manifold M of non-positive curvature. Write p:UM→M for the unit tangent bundle over M and let ℛ > denote the subset consisting of all vectors of higher rank. This subset is closed and invariant under the geodesic flow φ on UM. We define the structured dimension s-dim ℛ > which, essentially, is the dimension of the set p(ℛ > ) of base points of ℛ > .
The main result of this paper holds for manifolds with s-dim ℛ > <dim M/2: for every ε>0, there is an ε-dense, flow invariant, closed subset Ξ ε ⊂UM∖ℛ > such that p(Ξ ε )=M.

Abstract

Consider a closed, smooth manifold M of non-positive curvature. Write p:UM→M for the unit tangent bundle over M and let ℛ > denote the subset consisting of all vectors of higher rank. This subset is closed and invariant under the geodesic flow φ on UM. We define the structured dimension s-dim ℛ > which, essentially, is the dimension of the set p(ℛ > ) of base points of ℛ > .
The main result of this paper holds for manifolds with s-dim ℛ > <dim M/2: for every ε>0, there is an ε-dense, flow invariant, closed subset Ξ ε ⊂UM∖ℛ > such that p(Ξ ε )=M.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:06 Dec 2017 20:48
Publisher:Cambridge University Press
ISSN:0143-3857
Additional Information:Copyright © 2004 Cambridge University Press
Publisher DOI:https://doi.org/10.1017/S0143385704000197
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2106774
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1127.53070

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