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

Keith Burns, Howard Weiss

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

For any ε > 0, we construct an explicit smooth Riemannian metric on the sphere Sn, n ≥ 3, that is within ε of the round metric and has a geodesic for which the corresponding orbit of the geodesic flow is ε-dense in the unit tangent bundle. Moreover, for any ε > 0, we construct a smooth Riemannian metric on Sn, n ≥ 3, that is within ε 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 ε.

Original languageEnglish (US)
Pages (from-to)329-348
Number of pages20
JournalErgodic Theory and Dynamical Systems
Volume22
Issue number2
DOIs
StatePublished - Aug 26 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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