Growth of the number of geodesics between points and insecurity for Riemannian manifolds
Department of Mathematics, Northwestern University, Evanston, IL 60208-2730
IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil
We derive from this that a compact Riemannian manifold with no conjugate points whose geodesic flow has positive topological entropy is totally insecure: the geodesics between any pair of points cannot be blocked by a finite number of point obstacles.
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