Geodesic
Calculation of the Fomenko–Zieschang invariants in the
Sbornik. Mathematics, Tome 198 (2007) no. 8, pp. 1119-1143 
P. V. Morozov. Calculation of the Fomenko–Zieschang invariants in the. Sbornik. Mathematics, Tome 198 (2007) no. 8, pp. 1119-1143. http://geodesic.mathdoc.fr/item/SM_2007_198_8_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

All the Fomenko–Zieschang invariants are calculated in the Kovalevskaya–Yehia integrable case of the problem of the motion of a heavy gyrostat in a gravitational field; the topological classification of the non-degenerate equilibria of this system is obtained and the loop molecules of all the singularities are calculated. Bibliography: 10 titles.

[1] A. T. Fomenko, Kh. Tsishang, “Topologicheskii invariant i kriterii ekvivalentnosti integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody”, Izv. RAN. Ser. matem., 54:3 (1990), 546–575 ; A. T. Fomenko, Kh. Tsishang, “A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom”, Math. USSR-Izv., 36:3 (1991), 567–596 | MR | Zbl | DOI | Zbl

[2] A. V. Bolsinov, S. V. Matveev, A. T. Fomenko, “Topologicheskaya klassifikatsiya integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody. Spisok sistem maloi slozhnosti”, UMN, 45:2 (1990), 49–77 | MR | Zbl

[3] A. V. Bolsinov, A. T. Fomenko, Integriruemye gamiltonovy sistemy. Geometriya, topologiya, klassifikatsiya, t. 1, 2, Izd-vo UdGU, Izhevsk, 1999 ; A. V. Bolsinov, A. T. Fomenko, Integrable Hamiltonian systems. Geometry, topology, classification, vol. 1, 2, Chapman Hall, Boca Raton, FL, 2004 | MR | Zbl | MR | Zbl

[4] M. P. Kharlamov, P. E. Ryabov, “Bifurkatsii pervykh integralov v sluchae Kovalevskoi–Yakhi”, RKhD, 2:2 (1997), 25–40 | MR | Zbl

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

[6] P. V. Morozov, “Liuvilleva klassifikatsiya integriruemykh sistem sluchaya Klebsha”, Matem. sb., 193:10 (2002), 113–138 | MR | Zbl

[7] P. V. Morozov, “Topologiya sloenii Liuvillya sluchaev integriruemosti Steklova i Sokolova uravnenii Kirkhgofa”, Matem. sb., 195:3 (2004), 69–114 | MR | Zbl

[8] P. I. Topalov, “Vychislenie tonkogo invarianta Fomenko–Tsishanga dlya osnovnykh integriruemykh sluchaev dvizheniya tverdogo tela”, Matem. sb., 187:3 (1996), 143–160 | MR | Zbl

[9] H. Yehia, “New integrable cases in the dynamics of rigid bodies”, Mech. Res. Comm., 13:3 (1986), 169–172 | DOI | MR | Zbl

[10] Kh. M. Yakhya, “Novye integriruemye sluchai zadachi o dvizhenii girostata”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 4 (1987), 88–90