Analytic classification of singularities in the integrable Kowalevski–Yehia case
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 25-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we give analytic classification of singularities of the momentum map for integrable Kowalevski–Yehia case in rigid body dynamics.
Keywords: integrable Hamiltonian system, momentum map, bifurcation diagram, type of non-degenerate singularity.
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P. E. Ryabov. Analytic classification of singularities in the integrable Kowalevski–Yehia case. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 25-30. http://geodesic.mathdoc.fr/item/VUU_2010_4_a2/

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

[2] Ryabov P. E., Nekotorye sluchai vyrozhdeniya peremennykh v odnoi zadache o dvizhenii tverdogo tela vokrug nepodvizhnoi tochki, Dep. v VINITI No 3660-V91, 1991, 9 pp.

[3] Gashenenko I. N., “Bifurkatsionnoe mnozhestvo zadachi o dvizhenii girostata, podchinennogo usloviyam Kovalevskoi”, Mekhanika tverdogo tela, 27, Donetsk, 1995, 31–35 | MR | Zbl

[4] Kharlamov P. V., Lektsii po dinamike tverdogo tela, Izd-ie NGU, Novosibirsk, 1965, 221 pp.

[5] Kharlamov P. V., “Odin sluchai integriruemosti uravnenii dvizheniya tverdogo tela, imeyuschego nepodvizhnuyu tochku”, Mekhanika tverdogo tela, 3, Donetsk, 1971, 57–64

[6] Kharlamov M. P., Kharlamova I. I., Shvedov E. G., “Bifurkatsionnye diagrammy na izoenergeticheskikh urovnyakh girostata Kovalevskoi–Yakhya”, Mekhanika tverdogo tela, 40, Donetsk, 2010 (to appear)

[7] Kharlamov M. P., “Kriticheskie podsistemy girostata Kovalevskoi v dvukh postoyannykh polyakh”, Nelineinaya dinamika, 3:3 (2007), 331–348

[8] Ryabov P. E., Bifurkatsionnoe mnozhestvo zadachi o dvizhenii tverdogo tela vokrug nepodvizhnoi tochki v sluchae Kovalevskoi–Yakhi, Diss. $\dots$ kand. fiz.-mat. nauk, MGU, M., 1997, 143 pp.

[9] Bolsinov A. V., Fomenko A. T., Integriruemye gamiltonovy sistemy. Geometriya, topologiya, klassifikatsiya, v. 1, 2, Izd-vo RKhD, Izhevsk, 1999 | MR | Zbl

[10] Milnor Dzh., Teoriya Morsa, Izd-vo “Mir”, M., 1963, 185 pp. | MR