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

Abstract:
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 $\ep$.

This article is available in the following formats:

• Tex file
• dvi file
• Postscript file
• pdf file

• A surface with positive curvature and positive topological entropy by Gerhard Knieper and Howard Weiss. This paper is published in Journal of Differential Geometry 39(1994), 229-249.

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.