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Boundary effects on the magnetic Hamiltonian dynamics in two dimensions. (English) Zbl 1435.70034

Summary: We study the Hamiltonian dynamics of a charged particle submitted to a pure magnetic field in a two-dimensional domain. We provide conditions on the magnetic field in a neighbourhood of the boundary to ensure the con finement of the particle. We also prove a formula for the scattering angle in the case of radial magnetic fields.

MSC:

70H05 Hamilton’s equations
37N05 Dynamical systems in classical and celestial mechanics
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