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# Buyalo, S; Schroeder, V (2002). Invariant subsets of rank 1 manifolds. Manuscripta Mathematica, 107(1):73-88.

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## Abstract

It is proved that for a Riemannian manifold M with nonpositive sectional curvature and finite volume the space of directions at each point in which geodesic rays avoid a sufficiently small neighborhood of a fixed rank 1 vector v∈UM looks very much like a generalized Sierpinski carpet. We also show for nonpositively curved manifolds M with dim M≥ 3 the existence of proper closed flow invariant subsets of the unit tangent bundle UM whose footpoint projection is the whole of M.

## Citations

1 citation in Web of Science®
1 citation in Scopus®