Geodesic
Homogeneous spaces with integrable $G$-invariant Hamiltonian flows
Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 511-523.

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Examples are constructed of homogeneous spaces $M$ with semisimple groups of motions $G$ for which all $G$-invariant Hamiltonian systems on $T^*M$ are integrable. Particular examples of such include affine symmetric spaces. Bibliography: 11 titles. 
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I. V. Mykytyuk. Homogeneous spaces with integrable $G$-invariant Hamiltonian flows. Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 511-523. http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a5/

[1] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1979 | MR

[2] Mischenko A. S., “Integrirovanie geodezicheskikh potokov na simmetricheskikh prostranstvakh”, Matem. zametki, 31:2 (1982), 257–262 | MR | Zbl

[3] Mischenko A. S., Fomenko A. T., “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz, 12:2 (1978), 46–56 | MR | Zbl

[4] Kostant B., “The principal three-dimensional subgroup and the Betti numbers of complex simple Lie group”, Amer. J. Math., 81:4 (1959), 973–1032 | DOI | MR | Zbl

[5] Kostant B., “Lie group representation in polynomial rings”, Amer. J. Math., 85:3 (1963), 327–404 | DOI | MR | Zbl

[6] Mischenko A. S., Fomenko A. T., “Integriruemost uravnenii Eilera na poluprostykh algebrakh Li”, Tr. semin. po vekt. tenz. analizu pri MGU, no. 19, 1979, 3–94 | Zbl

[7] Steinberg R., “Invariants of finite reflection groups”, Canad. J. Math., 12:4 (1960), 616–618 | MR | Zbl

[8] Jacobson N., “Completely reducible Lie algebras of linear transformation”, Proc. Amer. Math. Soc., 2:1 (1951), 105–113 | DOI | MR | Zbl

[9] Koh S. S., “On affine symmetric spaces”, Trans. Amer. Math. Soc., 119:2 (1965), 291–309 | DOI | MR | Zbl

[10] Mikityuk I. V., “Odnorodnye prostranstva s integriruemymi invariantnymi gamiltonovymi potokami”, Dokl. AN SSSR, 265:5 (1982), 1074–1078 | MR | Zbl

[11] Thimm A., “Über die Integrabilität geodätischer Flüsse auf homogenen Räumen”, Bonn. Math. Schr., 1980, no. 127, 1–80 | MR