On Generalized Relativistic Billiards in External Force Fields |
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Authors: | Deryabin M V Pustyl'nikov L D |
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Institution: | (1) Department of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia;(2) Keldysh Institute of Applied Mathematics of RAS, Miusskaja sq. 4, 125047 Moscow, Russia;(3) University of Bielefeld, BiBoS, Postfach100131, D-33501 Bielefeld, Germany |
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Abstract: | In this Letter, we study generalized relativistic billiards: as a particle reflects from the boundary of the domain, its velocity is transformed as if the particle underwent an elastic collision with a moving wall, considered within 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 'monotone' action of the boundary. 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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Keywords: | energy exponential attractor force generalized relativistic billiards velocity |
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