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 language | English (US) |
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Pages (from-to) | 329-348 |
Number of pages | 20 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 22 |
Issue number | 2 |
DOIs | |
State | Published - Aug 26 2002 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics