Geodesic
Topological analysis of the two-centre problem on the two-dimensional
Sbornik. Mathematics, Tome 193 (2002) no. 8, pp. 1103-1138 Cet article a éte moissonné depuis la source Math-Net.Ru

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The two-centre problem on the two-dimensional sphere (with the standard metric of constant positive curvature) is investigated from the topological point of view. The Fomenko–Zieschang invariants are constructed, which completely describe the topology of the Liouville foliations on isoenergy surfaces of this system. Various types of motion in the configuration space (regular motions and limit motions corresponding to bifurcations of Liouville tori) are described. The connection between Fomenko–Zieschang invariants (marked molecules) and various types of motion is considered. 
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T. G. Vozmischeva; A. A. Oshemkov. Topological analysis of the two-centre problem on the two-dimensional. Sbornik. Mathematics, Tome 193 (2002) no. 8, pp. 1103-1138. http://geodesic.mathdoc.fr/item/SM_2002_193_8_a0/

[1] Lobachevskii N. I., “Novye nachala geometrii s polnoi teoriei parallelnykh”, Polnoe sobranie sochinenii, T. 2, GITTL, M.–L., 1949

[2] Chernikov N. A., “The Kepler problem in the Lobachevsky space and its solution”, Acta Phys. Polon. B, 23 (1992), 115–119 | MR

[3] Kozlov V. V., “O dinamike v prostranstvakh postoyannoi krivizny”, Vestn. MGU. Ser. 1. Matem., mekh., 1994, no. 2, 28–35 | MR | Zbl

[4] Kozlov V. V., Harin O. A., “Kepler's problem in constant curvature spaces”, Celestial Mech. Dynam. Astronom., 54 (1992), 393–399 | DOI | MR | Zbl

[5] Zhukovskii N. E., “O dvizhenii materialnoi psevdosfericheskoi figury po poverkhnosti psevdosfery”, Polnoe sobranie sochinenii, T. 1, ONTI NKTP SSSR, M.–L., 1937, 490–535

[6] Shrëdinger E., “Metod opredeleniya kvantovomekhanicheskikh sobstvennykh znachenii i sobstvennykh funktsii”, Izbrannye trudy po kvantovoi mekhanike, Nauka, M., 1976, 239–247

[7] Vozmischeva T. G., “Klassifikatsiya dvizhenii dlya obobscheniya zadachi Eilera na sferu”, Matematicheskii sbornik, Izd-vo UdGU, Izhevsk, 1998, 34–40

[8] Vozmischeva T. G., “Mathematical aspects in celestial mechanics, the Lagrange and Euler problems in the Lobachevsky space”, Proceedings of the international conference on geometry, integrability and quantization (Varna, Bulgaria, 1999), eds. I. M. Mladenov et al., Coral Press Sci. Publ., Sofia, 2000, 283–298 | MR | Zbl

[9] Vozmischeva T. G., “Classification of motions for generalization of the two center problem on a sphere”, Celestial Mech. Dynam. Astronom., 77 (2000), 37–48 | DOI | Zbl

[10] Shepetilov A. V., “Reduction of the two-body problem with central interaction on simply connected spaces of constant sectional curvature”, J. Phys. A, 31 (1998), 6279–6291 | DOI | MR

[11] Perelomov A. M., Integriruemye sistemy klassicheskoi mekhaniki i algebry Li, Nauka, M., 1990 | Zbl

[12] Higgs P. W., “Dynamical symmetries in a spherical geometry, I”, J. Phys. A, 12:3 (1979), 309–323 | DOI | MR | Zbl

[13] Arkhangelskii Yu. A., Analiticheskaya dinamika tverdogo tela, Nauka, M., 1977 | MR

[14] Levi-Chivita T., “Sur la résolution qualitative du problème restreint des trois corps”, Acta Math., 30 (1906), 305–327 | DOI | MR

[15] Bolsinov A. V., Fomenko A. T., Integriruemye gamiltonovy sistemy, T. 1, 2, Izdatelskii dom “Udmurtskii universitet”, Izhevsk, 1999 | MR | Zbl

[16] Bolsinov A. V., Rikhter P., Fomenko A. T., “Metod krugovykh molekul i topologiya volchka Kovalevskoi”, Matem. sb., 191:2 (2000), 3–42 | MR | Zbl

[17] Duboshin A. G., Nebesnaya mekhanika. Analiticheskie i kachestvennye metody, Nauka, M., 1964 | Zbl