On the growth of the number of geodesics joining two points

Authors: Keith Burns and Gabriel Paternain

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.

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


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

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