Geodesic
New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 78-86.

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

The integrability of certain classes of homogeneous geodesic, potential, and dissipative dynamical systems on the tangent bundles of finite-dimensional manifolds is shown. In this case, the force fields lead to variable-sign dissipation and generalize previously considered fields.
Keywords: dynamical system, geodesics, potential, integrability, dissipation, transcendental first integral. 
@article{DANMA_2021_500_a14,
     author = {M. V. Shamolin},
     title = {New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {78--86},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a14/}
}
TY  - JOUR
AU  - M. V. Shamolin
TI  - New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 78
EP  - 86
VL  - 500
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_500_a14/
LA  - ru
ID  - DANMA_2021_500_a14
ER  - 
%0 Journal Article
%A M. V. Shamolin
%T New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 78-86
%V 500
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2021_500_a14/
%G ru
%F DANMA_2021_500_a14
M. V. Shamolin. New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 78-86. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a14/

[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 mnogomernogo mnogoobraziya”, DAN, 482:5 (2018), 527–533

[4] Kozlov V.V., “Tenzornye invarianty i integrirovanie differentsialnykh uravnenii”, Uspekhi matem. nauk, 74:1 (2019), 117–148 | DOI | MR | Zbl

[5] Borisov A.V., Mamaev I.S., Sovremennye metody teorii integriruemykh sistem, In-t kompyuternykh issledovanii, M.-Izhevsk, 2003, 294 pp. | MR

[6] Novikov S.P., Taimanov I.A., Sovremennye geometricheskie struktury i polya, MTsNMO, M., 2005, 584 pp.

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

[8] Klein F., Neevklidova geometriya, Per. s nem., 4-e izd., ispr., obnovl., URSS, M., 2017, 352 pp.

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

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

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

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

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

[14] Shamolin M.V., “Novye sluchai odnorodnykh integriruemykh sistem s dissipatsiei na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Doklady RAN. Matematika, informatika, protsessy upravleniya, 495:1 (2020), 84–90 | DOI | Zbl

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