Geodesic
Estimate of the number of collisions of $n$ elastic particles on a~line
Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 1, pp. 64-78

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An explicit upper bound is obtained for the number of reflections of a billiard trajectory in a multidimensional polyhedral angle (in particular, for the number of collisions of $n$ elastic particles on a line) in terms of a special geometrical characteristic of the angle. 
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     author = {M. B. Sevryuk},
     title = {Estimate of the number of collisions of $n$ elastic particles on a~line},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {64--78},
     publisher = {mathdoc},
     volume = {96},
     number = {1},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a4/}
}
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M. B. Sevryuk. Estimate of the number of collisions of $n$ elastic particles on a~line. Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 1, pp. 64-78. http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a4/