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Periodic trajectories of a billiard in magnetic field. (Russian, English) Zbl 1100.70519
Prikl. Mat. Mekh. 69, No. 6, 942-949 (2005); translation in J. Appl. Math. Mech. 69, No. 6, 844-851 (2005).
The authors consider a problem on existence of periodic trajectories of a charged particle in magnetic field when the particle moves inside closed convex domain and is reflected elastically from its boundary. By means of geometric Poincaré theorem the presence of an infinite number of different periodic trajectories is established at small strength of magnetic field. Stability conditions are established for two-link trajectories in the case of homogeneous magnetic field.

70H05 Hamilton’s equations
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
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