Minimal geodesics
Author:
- 1 June 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 10 (2) , 263-286
Abstract
Motivated by the close relation between Aubry-Mather theory and minimal geodesies on a 2-torus we study the existence and properties of minimal geodesics in compact Riemannian manifolds of dimension ≥3. We prove that there exist minimal geodesics with certain rotation vectors and that there are restrictions on the rotation vectors of arbitrary minimal geodesics. A detailed analysis of the minimal geodesics of the ‘Hedlund examples’ shows that – to a certain extent – our results are optimal.Keywords
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