Geodesic
Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2006), pp. 42-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{IVM_2006_8_a5,
     author = {A. A. Magazev and I. V. Shirokov},
     title = {Hamiltonian systems in variations and the integration of the {Jacobi} equation on homogeneous spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {42--53},
     year = {2006},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2006_8_a5/}
}
TY  - JOUR
AU  - A. A. Magazev
AU  - I. V. Shirokov
TI  - Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2006
SP  - 42
EP  - 53
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/IVM_2006_8_a5/
LA  - ru
ID  - IVM_2006_8_a5
ER  - 
%0 Journal Article
%A A. A. Magazev
%A I. V. Shirokov
%T Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2006
%P 42-53
%N 8
%U http://geodesic.mathdoc.fr/item/IVM_2006_8_a5/
%G ru
%F IVM_2006_8_a5
A. A. Magazev; I. V. Shirokov. Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2006), pp. 42-53. http://geodesic.mathdoc.fr/item/IVM_2006_8_a5/

[1] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, T. II, Nauka, M., 1981, 416 pp.

[2] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989, 472 pp. | MR

[3] Vaisman I., “Second order Hamiltonian vector fields on tangent bundles”, Diff. Geom. and Appl., 5 (1995), 153–170 | DOI | MR | Zbl

[4] Mitric G., Vaisman I., “Poisson structures on tangent bundles”, Diff. Geom. and Appl., 18 (2003), 207–228 | DOI | MR | Zbl

[5] Vorobev Yu. M., “Gamiltonovy struktury sistem v variatsiyakh i simplekticheskie svyaznosti”, Matem. sb., 191:4 (2000), 3–28 | MR

[6] Bolsinov A. V., Iovanovich B., “Integriruemye geodezicheskie potoki na odnorodnykh prostranstvakh”, Matem. sb., 192:7 (2001), 21–40 | MR | Zbl

[7] Magazev A. A., Shirokov I. V., “Integrirovanie geodezicheskikh potokov na odnorodnykh prostranstvakh. Sluchai dikoi gruppy Li”, Teor. i matem. fiz., 136:3 (2003), 365–379 | MR

[8] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Prostranstva nad algebrami, Izd-vo Kazansk. un-ta, Kazan, 1985, 264 pp. | MR

[9] Trofimov V. V., Fomenko A. T., Algebra i geometriya integriruemykh gamiltonovykh differentsialnykh uravnenii, Faktorial, M., 1995, 439 pp. | MR | Zbl

[10] Kolar I., Michor P. W., Slovak J., Natural operations in differential geometry, Springer-Verlag, 1993, 434 pp. | MR

[11] Shirokov I. V., “Tozhdestva i invariantnye operatory na odnorodnykh prostranstvakh”, Teor. i matem. fiz., 126:3 (2001), 393–408 | MR | Zbl

[12] Karasev M. V., Maslov V. P., Nelineinye skobki Puassona. Geometriya i kvantovanie, Nauka, M., 1991, 368 pp. | MR | Zbl

[13] Shirokov I. V., “Koordinaty Darbu na $\mathrm{K}$-orbitakh i spektry operatorov Kazimira na gruppakh Li”, Teor. i matem. fiz., 123:3 (2000), 407–423 | MR | Zbl