Abstract
We state and prove rigorous mathematical results on the orbital stability of certain rectilinear trajectories of sufficiently energetic particles subjected to appropriate periodic potentials. This is done in the context of nontrivial classical Hamiltonian models, nonrelativistic and relativistic, in two space dimensions. The main steps involved in the proofs are the derivation of the asymptotic form of certain canonical maps in the plane in the limit of large particle energies and the application of a version of Moser’s twist theorem. When suitably specialized, these results establish rigorously for the first time that the pertinent straight-line channeling trajectories of fast particles in two-dimensional rigid crystal lattices have this stability property under reasonable conditions on the crystal potential.
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