Geodesic
New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 497 (2021), pp. 23-30.

Voir la notice de l'article provenant de la source Math-Net.Ru

The integrability of certain classes of homogeneous dynamical systems on the tangent bundles of four-dimensional manifolds is shown. The force fields involved in the systems lead to dissipation of variable sign and generalize previously considered fields.
Keywords: dynamical system, integrability, dissipation, transcendental first integral. 
@article{DANMA_2021_497_a4,
     author = {M. V. Shamolin},
     title = {New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {23--30},
     publisher = {mathdoc},
     volume = {497},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_497_a4/}
}
TY  - JOUR
AU  - M. V. Shamolin
TI  - New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 23
EP  - 30
VL  - 497
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_497_a4/
LA  - ru
ID  - DANMA_2021_497_a4
ER  - 
%0 Journal Article
%A M. V. Shamolin
%T New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 23-30
%V 497
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2021_497_a4/
%G ru
%F DANMA_2021_497_a4
M. V. Shamolin. New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 497 (2021), pp. 23-30. http://geodesic.mathdoc.fr/item/DANMA_2021_497_a4/

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

[2] Shamolin M.V., “Novye sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii k mnogomernoi sfere”, DAN, 474:2 (2017), 177–181 | MR

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

[4] Kozlov V.V., “Ratsionalnye integraly kvaziodnorodnykh dinamicheskikh sistem”, Prikl. matem. i mekhan., 79:3 (2015), 307–316 | Zbl

[5] Klein F., Neevklidova geometriya, Per. s nem., Izd. 4, ispr., obnovl., URSS, M., 2017, 352 pp.

[6] Veil G., Simmetriya, URSS, M., 2007

[7] Kozlov V.V., “Integriruemost i neintegriruemost v gamiltonovoi mekhanike”, Uspekhi matem. nauk, 38:1 (1983), 3–67 | MR | Zbl

[8] Puankare A., O krivykh, opredelyaemykh differentsialnymi uravneniyami, OGIZ, M.-L., 1947

[9] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1976

[10] Trofimov V.V., Shamolin M.V., “Geometricheskie i dinamicheskie invarianty integriruemykh gamiltonovykh i dissipativnykh sistem”, Fundam. i prikl. matem., 16:4 (2010), 3–229

[11] Shamolin M.V., “Novye sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii mnogomernogo mnogoobraziya”, DAN, 482:5 (2018), 527–533

[12] Shabat B.V., Vvedenie v kompleksnyi analiz, Nauka, M., 1987 | MR