02-282 M.V.Deryabin, L.D.Pustyl'nikov

Generalized relativistic billiards in external force fields (277K, PostScript) Jun 28, 02

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Abstract. In this paper we study generalized billiards, in which, as the particle reflects from the boundary of the domain, its velocity is transformed as in an elastic collision with a moving wall, considered in the framework of the special theory of relativity. Inside the domain the particle moves under the influence of some gravitational and non-gravitational force fields. We study both periodic and general non-periodic action of the boundary, and also the relativistic analogue of the accelerating model in the gravitational field. We prove that under some general conditions the invariant manifold in the velocity phase space of the generalized billiard, where the point velocity equals the velocity of light, is an exponential attractor, and for an open set of initial conditions the particle energy tends to infinity.

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