 02282 M.V.Deryabin, L.D.Pustyl'nikov
 Generalized relativistic billiards in external force fields
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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
nongravitational force fields.
We study both periodic and general nonperiodic 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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