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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{TMF_1993_96_1_a4,
     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},
     year = {1993},
     volume = {96},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a4/}
}
TY  - JOUR
AU  - M. B. Sevryuk
TI  - Estimate of the number of collisions of $n$ elastic particles on a line
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 64
EP  - 78
VL  - 96
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a4/
LA  - ru
ID  - TMF_1993_96_1_a4
ER  - 
%0 Journal Article
%A M. B. Sevryuk
%T Estimate of the number of collisions of $n$ elastic particles on a line
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 64-78
%V 96
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a4/
%G ru
%F TMF_1993_96_1_a4
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/

[1] Sinai Ya. G., Usp. matem. nauk, 33:1 (1978), 229–230 | MR | Zbl

[2] Galperin G. A., Usp. matem. nauk, 33:1 (1978), 211–212 | MR | Zbl

[3] Zemlyakov A. N., Kvant, 1978, no. 4, 14–21

[4] Galperin G. A., Zemlyakov A. N., Matematicheskie bilyardy, Nauka, M., 1990 | MR

[5] Galperin G. A., Chernov N. I., Billiardy i khaos, Znanie, M., 1991 | MR

[6] Galperin G. A., Tr. Mosk. matem. ob-va, 43 (1981), 142–196 | MR | Zbl

[7] Kozlov V. V., Treschev D. V., Billiardy. Geneticheskoe vvedenie v dinamiku sistem s udarami, MGU, M., 1991 | MR | Zbl

[8] Galperin G. A., DAN SSSR, 245:2 (1979), 285–288 | MR | Zbl

[9] Vaserstein L. N., Commun. Math. Phys., 69:1 (1979), 31–56 | DOI | MR

[10] Shin H. K., J. Chem. Phys., 62:10 (1975), 4130–4137 | DOI

[11] Azriel V. M., Rusin L. Yu., Sevryuk M. B., Proc. Eighth Symp. Atomic and Surface Physics (SASP-92) (Trento), 1992, 2.14–2.19

[12] Azriel V. M.,Rusin L. Yu.,Sevryuk M. B., Orientanionnye effekty v protsessakh peredachi energii pri mnogokratnykh soudareniyakh v sisteme trekh chastits: sravnenie traektornogo scheta i vychislenii v impulsnom priblizhenii, dep. v VINITI 1135-V92, INEP KhF RAN., M., 1992

[13] Maergoiz A. I., Nikitin E. E., Rusin L. Yu., “Dinamika obrazovaniya ionov pri stolknovitelnoi dissotsiatsii dvukhatomnykh molekul”, Khimiya plazmy, vyp. 12, Energoatomizdat, M., 1985, 3–55

[14] Safron S. A., J. Phys. Chem., 89:26 (1985), 5713–5719 | DOI

[15] Gislason E. A., Sizun M., J. Phys. Chem., 95:22 (1991), 8462–8466 | DOI

[16] Lenin L. V., Rusin L. Yu., Sevryuk M. B., Protsessy dissotsiatsii i kompleksoobrazovaniya pri stolknoveniyakh molekul galogenidov tseziya s atomami inertnykh gazov i rtuti: impulsnaya model, dep. v VINITI 4652-V91, INEP KhF RAN, M., 1991