Scattering in multiparticle and billiard dynamical systems

A. Yu. Plakhov   ; A. M. Stepin

Sbornik. Mathematics, Tome 190 (1999) no. 7, pp. 1005-1033

Résumé

The object of study is scattering in billiard dynamical systems and in multiparticle systems on a line (with potential interaction). There exist examples in which the scattering map for such systems is triangular, that is, the corresponding Jacobi matrix has block-triangular form. In this paper it is proved that the billiard scattering in a convex polyhedral cone is triangular if and only if the cone is the closure of some chamber of a Coxeter group. All systems of masses for which multiparticle systems with billiard interaction have triangle scattering are listed. Further, it is proved for multiparticle systems with repulsive interaction that the system of masses of the particles must belong to this list in the case of triangular scattering. Convex plane domains in which the billiards have a triangular scattering map are characterized.

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