Growth of the number of geodesics between points and insecurity for riemannian manifolds

Details Growth of the number of geodesics between points and insecurity for riemannian manifolds Growth of the number of geodesics between points and insecurity for riemannian manifolds

2007-01-20

arxiv.org/abs/math/0701579v1

Discrete and Continuous Dynamical Systems A 21 (2008), 403 -- 413

Mathematics

Dynamical Systems

14 pages, 0 figures

Scientific paper

A Riemannian manifold is said to be uniformly secure if there is a finite number $s$ such that all geodesics connecting an arbitrary pair of points in the manifold can be blocked by $s$ point obstacles. We prove that the number of geodesics with length $\leq T$ between every pair of points in a uniformly secure manifold grows polynomially as $T \to \infty$. 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.

Affiliated with

Also associated with

No associations

Rating

Growth of the number of geodesics between points and insecurity for riemannian manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Growth of the number of geodesics between points and insecurity for riemannian manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Growth of the number of geodesics between points and insecurity for riemannian manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375342