Geodesic
Periodic trajectories in three-dimensional Birkhoffs billiards
Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 1-13 
I. K. Babenko. Periodic trajectories in three-dimensional Birkhoffs billiards. Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 1-13. http://geodesic.mathdoc.fr/item/SM_1992_71_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A lower bound is given for the number of periodic trajectories inside a strictly convex domain in three dimensional space.

[1] Birkgof G., Dinamicheskie sistemy, Gostekhizdat, M.–L., 1941

[2] Kornfeld I. P., Sinai Ya. G., Fomin S. V., Ergodicheskaya teoriya, Nauka, M., 1980 | MR

[3] Treschev D. V., “K voprosu o periodicheskikh traektoriyakh bilyarda Birkgofa”, Vest. MGU. Ser. 1. Matem., mekh., 1987, no. 5, 72–76

[4] Bukhgolts N. N., Osnovnoi kurs teoreticheskoi mekhaniki, ch. II, GITTL, M.–L., 1939

[5] Fuks D. B., Fomenko A. T., Gutenmakher V. L., Gomotopicheskaya topologiya, Izd-vo MGU, M., 1969

[6] Ganea T., “On some numerical homotopy invariants”, Proc. of the Int. Congress of Math., 1962, 466–472 | MR

[7] Froloff S. V., Elsholz L. E., Limite inféricure pour le nombre des valeurs critiques d'une fonction, donné sur variété, ONTI, M.–L., 1935, S. 637–643

[8] Palais R. S., “Morse theory on Hilbert manifolds”, Topology, 2:4 (1963), 299–340 | DOI | MR | Zbl

[9] Wasserman A. G., “Equivariant differential topology”, Topology, 8:2 (1969), 127–150 | DOI | MR | Zbl

[10] Shvarts Dzh., Differentsialnaya geometriya i topologiya, Mir, M., 1970 | Zbl

[11] Kartan A., Eilenberg S., Gomologicheskaya algebra, IL, M., 1960

[12] Wall C. T. C., “Resolutions for extensions of groups”, Proc. Camb. Phil. Soc., 57:1 (1961), 251–255 | DOI | MR | Zbl

[13] Prakhar K., Raspredelenie prostykh chisel, Mir, M., 1967 | MR