Geodesic
Integrable systems with many degrees of freedom and with dissipation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2019), pp. 29-38
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this study, we show the integrability of certain classes of dynamic systems on the tangent bundle to a multi-dimensional manifold. In this case, the force fields have variable dissipation and generalize the cases considered previously. 
@article{VMUMM_2019_6_a4,
     author = {M. V. Shamolin},
     title = {Integrable systems with many degrees of freedom and with dissipation},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {29--38},
     year = {2019},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a4/}
}
TY  - JOUR
AU  - M. V. Shamolin
TI  - Integrable systems with many degrees of freedom and with dissipation
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 29
EP  - 38
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a4/
LA  - ru
ID  - VMUMM_2019_6_a4
ER  - 
%0 Journal Article
%A M. V. Shamolin
%T Integrable systems with many degrees of freedom and with dissipation
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 29-38
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a4/
%G ru
%F VMUMM_2019_6_a4
M. V. Shamolin. Integrable systems with many degrees of freedom and with dissipation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2019), pp. 29-38. http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a4/

[1] Shamolin M.V., “Malomernye i mnogomernye mayatniki v nekonservativnom pole. Ch. 1”, Itogi nauki i tekhniki. Ser. Sovremennaya matematika i ee prilozheniya. Tematicheskie obzory, 134, 2017, 6–128

[2] Shamolin M.V., “Malomernye i mnogomernye mayatniki v nekonservativnom pole. Ch. 2”, Itogi nauki i tekhniki. Ser. Sovremennaya matematika i ee prilozheniya. Tematicheskie obzory, 135, 2017, 3–93

[3] Shamolin M.V., “Novye sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii dvumernogo mnogoobraziya”, Dokl. RAN, 475:5 (2017), 519–523 | MR

[4] Shamolin M.V., “Novye sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Dokl. RAN, 477:2 (2017), 168–172 | DOI | MR

[5] Shamolin M.V., “Novye sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya”, Dokl. RAN, 479:3 (2018), 270–276 | DOI | MR

[6] Dubrovin B.A., Novikov S.P., Fomenko A.T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[7] Dubrovin B.A., Novikov S.P., “O skobkakh Puassona gidrodinamicheskogo tipa”, Dokl. AN SSSR, 219:2 (1984), 228–237

[8] Shabat B.V., Vvedenie v kompleksnyi analiz, Nauka, M., 1987

[9] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971

[10] Shamolin M.V., “Ob integriruemosti v transtsendentnykh funktsiyakh”, Uspekhi matem. nauk, 53:3 (1998), 209–210 | DOI | MR | Zbl

[11] Shamolin M.V., “Integriruemye sistemy s peremennoi dissipatsiei na kasatelnom rassloenii k mnogomernoi sfere i prilozheniya”, Fund. i prikl. matem., 20:4 (2015), 3–231 | MR