Complete involutive algebras of functions on cotangent bundles of homogeneous spaces

Mathematische Zeitschrift

Volumn 246, Issue 1-2, 2004, Pages 213-236

  Bolsinov, Alexey V ^a   Jovanović, Božidar ^b  

^a Department of Mechanics ^*  (Serbia)

^b MATHEMATICAL INSTITUTE   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0742271382     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00209-003-0596-x     Document Type: Article

References (48)

1. Aloff, S., Wallach, R.: An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures. Bull. Am. Math. Soc. 81 (1), 93-97 (1975)
2. Arnold, V.I., Kozlov, V.V., Neishtadt, A.I.: Mathematical Aspects of Classical and Celestial Mechanics. Dynamical Systems III, Springer, 1988
3. Babenko, I.K., Nekhoroshev, N.N.: Complex structures on two-dimensional tori that admit metrics with a nontrivial quadratic integral. Mat. Zametki 58 (5), 643-652 (Russian) (1995)
4. Bazaikin, Ya.V.: Double quotients of Lie groups with an integrable geodesic flows. Sibirsk. Mat. Zh. 41 (3), 513-530 (2000) (Russian); English translation: Siberian Math. J. 41 (3), 419-432 (2000)
5. Bolsinov, A.V.: Compatible Poisson brackets on Lie algebras and the completeness of families of functions in involution. Izv. Acad. Nauk SSSR, Sci. matem. 55(1), 68-92 (1991) (Russian); English translation: Math. USSR-Izv. 38 (1), 69-90 (1992)
6. Bolsinov, A.V.: Compatible Poisson brackets on Lie algebras and the completeness of families of functions in involution. Izv. Acad. Nauk SSSR, Sci. matem. 55(1), 68-92 (1991) (Russian); English translation: Math. USSR-Izv. 38 (1), 69-90 (1992)
7. 2 arising from integrable cases in the dynamics of a rigid body. Uspekhi Mat. Nauk 50 (3), 3-32 (1995) (Russian); English translation: Russ. Math. Surv. 50, 473-501 (1995)
8. 2 arising from integrable cases in the dynamics of a rigid body. Uspekhi Mat. Nauk 50 (3), 3-32 (1995) (Russian); English translation: Russ. Math. Surv. 50, 473-501 (1995)
9. Bolsinov, A.V., Taimanov, I.A.: Integrable geodesic flow with positive topological entropy. Invent. math. 140, 639-650 (2000); arXiv: math.DG/9905078
10. Bolsinov, A.V., Taimanov, I.A.: Integrable geodesic flows on the suspensions of toric automorphisms. Tr. Mat. Inst. Steklova 231, 46-63 (2000) (Russian); English translation: Proc. Steklov. Inst. Math. 231 (4), 42-58 (2000); arXiv: math.DG/9911193
11. Bolsinov, A.V., Jovanović, B.: Integrable geodesic flows on homogeneous spaces. Matem. Sbornik 192 (7), 21-40 (2001) (Russian): English translation: Sb. Mat. 192 (7-8), 951-969 (2001)
12. Bolsinov, A.V., Jovanović, B.: Non-commutative integrability, moment map and geodesic flows. Ann. Global Anal. Geom. 23 (4), 305-322 (2003); arXiv: math-ph/0109031
13. Bordemann, M.: Hamiltonsche Mechanik auf homogenen Räumen. Diplomarbeit, Fakultät für Physik, Universität Freiburg, May 1985
14. Brailov, A.V.: Construction of complete integrable geodesic flows on compact symmetric spaces. Izv. Acad. Nauk SSSR, Ser. matem. 50 (2), 661-674 (1986) (Rfussian); English translation: Math. USSR-Izv
15. Brailov, A.V.: Construction of complete integrable geodesic flows on compact symmetric spaces. Izv. Acad. Nauk SSSR, Ser. matem. 50 (2), 661-674 (1986) (Rfussian); English translation: Math. USSR-Izv
16. Butler, L.: A new class of homogeneous manifolds with Liouville-integrable geodesic flows. C. R. Math. Acad. Sci. Soc. R. Can. 21 (4), 127-131 (1999)
17. Guillemin, V., Sternberg, S.: On collective complete integrability according to the method of Thimm. Ergod. Th. & Dynam. Sys. 3, 219-230 (1983)
18. Guillemin, V., Sternberg, S.: Symplectic techniques in Physics. Cambridge University Press, 1984
19. Jovanović, B.: Geometry and integrability of Euler-Poincaré-Suslov equations. Nonlinearity 14 (6), 1555-1657 (2001); arXiv: math-ph/0107024
20. Kiyohara, K.: Two-dimensional geodesic flows having first integrals of higher degree. Math. Ann. 320, 487-505 (2001)
21. Kruglikov, B.: Examples of integrable sub-Riemannian geodesic flows. J. Dynam. Control Systems. 8 (3), 323-340 (2002); arXiv: math.DS/0105128
22. Kolokol'tsov, V.N.: Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities. Izv. Akad. Nauk SSSR Ser. Mat. 46 (5), 994-1010 (1982) (Russian); English translation: Math. USSR Izv. 21, 291-306 (1983)
23. Kolokol'tsov, V.N.: Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities. Izv. Akad. Nauk SSSR Ser. Mat. 46 (5), 994-1010 (1982) (Russian); English translation: Math. USSR Izv. 21, 291-306 (1983)
24. Kramer, M.: Sphärische Untergruppen in kompakten zusammenhangenden Liegruppen. Compositio Math. 38, 129-153 (1979)
25. Mishchenko, A.S.: Integration of geodesic flows on symmetric spaces. Mat. zametki 31 (2), 257-262 (1982) (Russian); English translation: Math. Notes. 31 (1-2), 132-134 (1982)
26. Mishchenko, A.S., Fomenko, A.T.: Euler equations on finite-dimensional Lie groups. Izv. Acad. Nauk SSSR, Ser. matem. 42 (2), 396-415 (1978) (Russian); English translation: Math. USSR-Izv. 12 (2), 371-389 (1978)
27. Mishchenko, A.S., Fomenko, A.T.: Generalized Liouville method of integration of Hamiltonian systems. Funkts. Anal. Prilozh. 12 (2), 46-56 (1978) (Russian); English translation: Funct. Anal. Appl. 12, 113-121 (1978)
28. Mikityuk, I.V.: Homogeneous spaces with integrable G-invariant Hamiltonian flows. Izv. Acad. Nauk SSSR, Ser. Mat. 47 (6), 1248-1262 (1983) (Russian); English translation in Math. USSR-Izv.
29. Mikityuk, I.V.: Homogeneous spaces with integrable G-invariant Hamiltonian flows. Izv. Acad. Nauk SSSR, Ser. Mat. 47 (6), 1248-1262 (1983) (Russian); English translation in Math. USSR-Izv.
30. Mikityuk, I.V.: Integrability of the Euler equations associated with filtrations of semi-simple Lie algebras. Matem. Sbornik 125 (4), 167 (1984) (Russian); English translation: Math. USSR Sbornik 53 (2), 541-549 (1986)
31. Mikityuk, I.V.: Integrability of the Euler equations associated with filtrations of semi-simple Lie algebras. Matem. Sbornik 125 (4), 167 (1984) (Russian); English translation: Math. USSR Sbornik 53 (2), 541-549 (1986)
32. Mykytyuk, I.V., Stepin, A.M.: Classification of almost spherical pairs of compact simple Lie groups. In: Poisson geometry, Banach Center Publ., 51, Polish Acad. Sci., Warsaw, 2000, pp. 231-241
33. Mykytyuk, I.V.: Actions of Borel subgroups on homogeneous spaces of reductive complex Lie groups and integrability. Composito Math. 127, 55-67 (2001)
34. Panyushev, D.I.: Complexity of quasiaffine homogeneous varieties, t-decompositions, and affine homogeneous spaces of complexity 1, Adv. in Soviet Math. 8, 151-166 (1992)
35. Paternain, G.P., Spatzier, R.J.: New examples of manifolds with completely integrable geodesic flows. Adv. in Math. 108, 346-366 (1994); arXiv: math.DS/9201276
36. 2 and the case of Goryachev-Chaplygin. Commun. Math. Phys. 207, 641-663 (1999)
37. 2 possessing an integral of fourth degree in momenta. Ann. Global Anal. Geom. Math. 17, 201-219 (1999)
38. Strichartz, R.S.: Sub-Riemannian geometry. J. Diff. Geometry, 24, 221-263 (1986); 30, 595-596 (1989)
39. Strichartz, R.S.: Sub-Riemannian geometry. J. Diff. Geometry, 24, 221-263 (1986); 30, 595-596 (1989)
40. Taimanov, I.A.: Topological obstructions to integrability of geodesic flows on nonsimply-connected manifolds. Izv. Acad. Nauk SSSR, Ser. matem. 51 (2), 429-435 (1987) (Russian); English translation: Math. USSR-Izv., 30 (2), 403-409 (1988)
41. Taimanov, I.A.: Topological obstructions to integrability of geodesic flows on nonsimply-connected manifolds. Izv. Acad. Nauk SSSR, Ser. matem. 51 (2), 429-435 (1987) (Russian); English translation: Math. USSR-Izv., 30 (2), 403-409 (1988)
42. Taimanov, I.A.: Integrable geodesic flows of nonholonomic metrics. J. Dynamical and Control Systems, 3 (1), 129-147 (1997); arXiv: dg-ga/9610012
43. Thimm, A.: Integrable geodesic flows on homogeneous spaces. Ergod. Th. & Dynam. Sys. 1, 495-517 (1981)
44. Trofimov, V.V.: Euler equations on Borel subalgebras of semisimple Lie groups. Izv. Acad. Nauk SSSR, Ser. matem., 43 (3), 714-732 (1979) (Russian). English translation: Math. USSR-Izv.
45. Trofimov, V.V.: Euler equations on Borel subalgebras of semisimple Lie groups. Izv. Acad. Nauk SSSR, Ser. matem., 43 (3), 714-732 (1979) (Russian). English translation: Math. USSR-Izv.
46. Trofimov, V.V., Fomenko, A.T.: Algebra and geometry of integrable Hamiltonian differential equations. Moscow, Faktorial, 1995 (Russian)
47. Vinberg, E.B.: Commutative homogeneous spaces and co-isotropic symplectic actions. Uspekhi Mat. Nauk 56 (1), 3-62 (2001) (Russian); English translation: Russian Math. Surveys 56 (1), 1-60 (2001)
48. Vinberg, E.B.: Commutative homogeneous spaces and co-isotropic symplectic actions. Uspekhi Mat. Nauk 56 (1), 3-62 (2001) (Russian); English translation: Russian Math. Surveys 56 (1), 1-60 (2001)