Spheres with positive curvature and nearly dense orbits of the geodesic flow

Authors: Keith Burns and Howard Weiss

For any $\ep > 0$, we construct a smooth Riemannian metric on the sphere $S^3$ that is within $\ep$ of the round metric and has a geodesic for which the corresponding orbit of the geodesic flow is $\ep$-dense in the unit tangent bundle. Moreover we construct an orbit of the geodesic flow such that the complement of the orbit closure has Liouville measure less than $\ep$.

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The paper will be appearing in Ergodic Theory and Dynamical Systems. A closely related article is

Authors' addresses:
	Keith  Burns 
	Department of Mathematics
	Northwestern University
	Evanston, IL 60208-2730
        burns followed by math.northwestern.edu

        Howard Weiss
        Mathematics Department
        Pennsylvania State University
        University Park, PA 16802       
        weiss followed by math.psu.edu.

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