Geodesic
Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 2, pp. 5-20 
A. Yu. Anikin; J. Brüning; S. Yu. Dobrokhotov. Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 2, pp. 5-20. http://geodesic.mathdoc.fr/item/FPM_2015_20_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a $2$-dimensional Hamiltonian system describing classical electron motion in a graphene placed in a large constant magnetic field and an electric field with a periodic potential. Using the Maupertuis–Jacobi correspondence and an assumption that the magnetic field is large, we make averaging and reduce the original system to a $1$-dimensional Hamiltonian system on the torus. This allows us to describe the trajectories of both systems and classify them by means of Reeb graphs.

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