Bangert, Victor (1990). Minimal geodesics. Ergodic theory & dynamical systems, 10(2), pp. 263-286. Cambridge University Press 10.1017/S014338570000554X
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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.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
ISSN: |
0143-3857 |
Publisher: |
Cambridge University Press |
Language: |
English |
Submitter: |
Marceline Brodmann |
Date Deposited: |
28 Jul 2020 09:15 |
Last Modified: |
28 Jul 2020 09:15 |
Publisher DOI: |
10.1017/S014338570000554X |
BORIS DOI: |
10.7892/boris.115451 |
URI: |
https://boris.unibe.ch/id/eprint/115451 |
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