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2000 | 51 | 1 | 231-241
Tytuł artykułu

Classification of almost spherical pairs of compact simple Lie groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
All homogeneous spaces G/K (G is a simple connected compact Lie group, K a connected closed subgroup) are enumerated for which arbitrary Hamiltonian flows on T*(G/K) with G-invariant Hamiltonians are integrable in the class of Noether integrals and G-invariant functions.
Słowa kluczowe
Rocznik
Tom
51
Numer
1
Strony
231-241
Opis fizyczny
Daty
wydano
2000
Twórcy
  • Department of Applied Mathematics, State University "L'viv Politechnica", S. Bandery 12, 79013 L'viv, Ukraine
  • Department of Mechanics and Mathematics, Moscow State University, 117234 Moscow, Russia
Bibliografia
  • [Ar] Sh. Araki, On root systems and infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1962), 90-126.
  • [Bo1] N. Bourbaki, Lie groups and algebras, I-III, Mir, Moscow, 1970 (in Russian).
  • [Bo2] N. Bourbaki, Lie groups and algebras, IV-VI, Mir, Moscow, 1972 (in Russian).
  • [Bo3] N. Bourbaki, Lie groups and algebras, VII,VIII, Mir, Moscow, 1978 (in Russian).
  • [Br] M. Brion, Classification des espaces homogenes spheriques, Compositio Math. 63 (1987), 189-208.
  • [Ch] M. L. Chumak, Integrable G-invariant Hamiltonian systems and uniform spaces with simple spectrum, Func. Anal. and its Applic. 20 (1986), 91-92.
  • [Dy1] E. B. Dynkin, Maximal subgroups of classical groups, Trudy Moskov. Mat. Obshchestva 1 (1952), 39-151 (in Russian); Am. Math. Soc. Transl. 2 (1957), 245-378.
  • [Dy2] E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Matem. Sbornik 30 (1952), 349-462 (in Russian); Am. Math. Soc. Transl. 2 (1957), 111-244.
  • [El] A. G. Elashvili, Canonical form and stationary subalgebras of points in general position of simple linear Lie groups, Func. Anal. and its Applic. 6 (1972), 51-62 (in Russian).
  • [GG] M. Goto and F. Grosshans, Semisimple Lie algebras, Vol. 38, Lecture Notes in Pure and Applied Math., New York and Basel, 1978.
  • [GS1] V. Guillemin and S. Sternberg, Multiplicity-free spaces, J. Differential Geometry 19 (1984), 31-56.
  • [GS2] V. Guillemin and S. Sternberg, On collective complete integrability according to the method of Thimm, Ergod. Theory and Dynam. Syst. 3 (1983), 219-230.
  • [GS3] V. Guillemin and S. Sternberg, Geometric asymptotics, AMS, Providence, Rhode Island, 1977.
  • [He] S. Helgason, Differential geometry and symmetric spaces, Academic Press, 1962.
  • [IW] K. Ii and S. Watanabe, Complete integrability of the geodesic flows on symmetric spaces, in: Geometry of Geodesics and Related Topics, Tokyo, K. Shiohama (ed.), North-Holland, 1984, 105-124.
  • [Kr] M. Kramer, Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen, Compositio Math. 38 (1979), 129-153.
  • [Mi] A. S. Mishchenko, Integration of geodesic flows on symmetric spaces, Mat. Zametki 32 (1982), 257-262 (in Russian).
  • [My1] I. V. Mykytiuk, Homogeneous spaces with integrable G-invariant Hamiltonian flows, Math. USSR Izvestiya 23 (1984), 511-523.
  • [My2] I. V. Mykytiuk, On the integrability of invariant Hamiltonian systems with homogeneous configuration spaces, Math. USSR Sbornik 57 (1987), 527-546.
  • [On] A. L. Onishchik, Inclusion relations between transitive compact transformation groups, Trudy Mosc. Matem. Obshchestva 11 (1962), 199-242 (in Russian).
  • [PM] A. K. Prykarpatsky and I. V. Mykytiuk, Algebraic integrability of nonlinear dynamical systems on manifolds. Classical and quantum aspects, Vol. 443, Math. and its Appl., Kluwer Academic Publishers, 1998.
  • [Ti] A. Timm, Integrable geodesic flows on homogeneous spaces, Ergod. Theory and Dynam. Syst. 1 (1981), 495-517.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv51z1p231bwm
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