New cases of integrable odd-order systems with dissipation
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 95-101.

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

This paper shows the integrability of certain classes of odd-order dynamical systems that are homogeneous with respect to some of the variables and in which a system on the tangent bundle of smooth manifolds is distinguished. In this case, the force fields have dissipation of different signs and generalize previously considered cases.
Keywords: dynamical system, integrability, dissipation, transcendental first integral.
@article{DANMA_2020_491_a19,
     author = {M. V. Shamolin},
     title = {New cases of integrable odd-order systems with dissipation},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {95--101},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a19/}
}
TY  - JOUR
AU  - M. V. Shamolin
TI  - New cases of integrable odd-order systems with dissipation
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 95
EP  - 101
VL  - 491
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_491_a19/
LA  - ru
ID  - DANMA_2020_491_a19
ER  - 
%0 Journal Article
%A M. V. Shamolin
%T New cases of integrable odd-order systems with dissipation
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 95-101
%V 491
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_491_a19/
%G ru
%F DANMA_2020_491_a19
M. V. Shamolin. New cases of integrable odd-order systems with dissipation. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 95-101. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a19/

[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 sedmogo poryadka s dissipatsiei”, DAN, 487:4 (2019), 381–386

[3] Shamolin M.V., “Novye sluchai integriruemykh sistem devyatogo poryadka s dissipatsiei”, DAN, 489:6 (2019), 592–598

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

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

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

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

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

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