Abstract
In chaos theory the separation of infinitesimally close trajectories has great importance. In present paper this behavior is investigated for classical magnetic billiard systems on Riemannian manifolds. The separation of the trajectories during the bounceless segments as well as at the reflections is studied generally, with a method similar to that of Jacobi fields for geodesic flows. For two-dimensional manifolds the results are also given in a natural coordinate frame, and they are illustrated in special (homogeneous) cases. We relate our issues to the known properties of the curvature of the horocycles, too.
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