Geodesic
Semiclassical electron motion and Novikov conjecture
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–2, Tome 235 (1996), pp. 228-234

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The structure of nonclosed trajectories of semiclassical electron motion in a crystal in a weak constant and uniform magnetic field of irrationality degree 3 is considered. It is proved that two cases can exist. In the first case the set of energy levels which contain nonclosed trajectories is a closed interval and any regular nonclosed trajectory lies in a finite-wide stripe and comes through it in one direction. In the other case, there is only one energy level containing nonclosed trajectories. Bibl. 5 titles. 
@article{ZNSL_1996_235_a10,
     author = {I. A. Dynnikov},
     title = {Semiclassical electron motion and {Novikov} conjecture},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {228--234},
     publisher = {mathdoc},
     volume = {235},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_235_a10/}
}
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I. A. Dynnikov. Semiclassical electron motion and Novikov conjecture. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–2, Tome 235 (1996), pp. 228-234. http://geodesic.mathdoc.fr/item/ZNSL_1996_235_a10/