On the growth of the number of geodesics joining two points

Abstract:
We construct a smooth metic on the sphere $S^2$, aritrarily close to the round metric, with a point $p$, not conjugate to itself along any geodesic, for which the number of geodesic loops based at $p$ with length at most $T$ grows as fast as we wish with $T$.

This article is in the proceedings of the International Congress on Dynamcial Systems held in Montevideo, Uruguay during March 1995. The reference is "International Congress on Dynamical Systems", edited by J. Lewowicz, F. Ledrappier and S. Newhouse, Pitman Lecture Notes in Mathematics 362, 7--20. The publisher is Addison Wesley Longman.

A closely related article is

• Counting geodesics on a Riemannian manifold and topological entropy of geodesic flows

Authors' addresses:
	Keith  Burns 
	Department of Mathematics
	Northwestern University
	Evanston, IL 60208-2730
        U.S.A.

	

        Gabriel Paternain
        DPMMS 
        Centre for Mathematical Sciences 
        University of Cambridge 
        Wilberforce Road 
        Cambridge CB3 0WB
        England