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Minimal geodesics†

Published online by Cambridge University Press:  19 September 2008

Victor Bangert
Victor Bangert
Affiliation:
Mathematisches Institut der Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 2 , June 1990 , pp. 263 - 286
Copyright
Copyright © Cambridge University Press 1990

References

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