98-693 Keith Burns and Howard Weiss
Spheres with positive curvature and nearly dense orbits for the geodesic flow (643K, Postscript) Oct 30, 98
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Abstract. For any \$\ep > 0\$, we construct an explicit smooth Riemannian metric on the sphere \$S^n, n \geq 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, for any \$\ep > 0\$, we construct a smooth Riemannian metric on \$S^n, n \geq 3\$, that is within \$\ep\$ of the round metric and has a geodesic for which the complement of the closure of the corresponding orbit of the geodesic flow has Liouville measure less than \$\ep\$.

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