Geodesic
On the continuability of solutions of autonomous differential systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 15-28.

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

Problems about a continuability of solutions of real autonomous systems of equations in total differentials and about a reducibility of such systems to many-dimensional dynamical systems are investigated. The reducibility criterion is proved. Conditions at which realisation the reducible system of exact differential equations has orbits–torus-cylinders, are received. Examples are given. When the received outcomes can be transferred on a complex case is noted.
Keywords: autonomous system, quite solvable system of the exact equations, continuability of the solutions, many-dimensional dynamical system
Mots-clés : orbit. 
@article{IVM_2020_11_a1,
     author = {V. V. Amel'kin and V. Yu. Tyshchenko},
     title = {On the continuability of solutions of autonomous differential systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--28},
     publisher = {mathdoc},
     number = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_11_a1/}
}
TY  - JOUR
AU  - V. V. Amel'kin
AU  - V. Yu. Tyshchenko
TI  - On the continuability of solutions of autonomous differential systems
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 15
EP  - 28
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_11_a1/
LA  - ru
ID  - IVM_2020_11_a1
ER  - 
%0 Journal Article
%A V. V. Amel'kin
%A V. Yu. Tyshchenko
%T On the continuability of solutions of autonomous differential systems
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 15-28
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_11_a1/
%G ru
%F IVM_2020_11_a1
V. V. Amel'kin; V. Yu. Tyshchenko. On the continuability of solutions of autonomous differential systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 15-28. http://geodesic.mathdoc.fr/item/IVM_2020_11_a1/

[1] Gaishun I. V., Vpolne razreshimye mnogomernye differentsialnye uravneniya, Editorial URSS, M., 2004

[2] Amelkin V. V., Differentsialnye uravneniya s “mnogomernym vremenem”. Avtonomnye i lineinye mnogomernye differentsialnye uravneniya, LAP LAMBERT Acad. Publ., Saarbrüchen, 2012

[3] Myshkis A. D., “O prodolzhenii reshenii uravnenii Pfaffa”, Differents. uravneniya, 21:8 (1985), 1331–1337 | MR | Zbl

[4] Cergeev I. N., “Prodolzhaemost reshenii differentsialnykh uravnenii do neprodolzhaemogo”, Differents. uravneniya, 52:6 (2016), 847–848

[5] Erugin N. P., Kniga dlya chteniya po obschemu kursu differentsialnykh uravnenii, Nauka i tekhn., Minsk, 1979 | MR

[6] Zubov V. I., Ustoichivost dvizheniya, Vyssh. shk., M., 1984 | MR

[7] Nemytskii V. V., “K teorii orbit obschikh dinamicheskikh sistem”, Matem. sb., 23:2 (1948), 161–186 | MR

[8] Nemytskii V. V., Stepanov V. V., Kachestvennaya teoriya differentsialnykh uravnenii, GITTL, M.–L., 1949 | MR

[9] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1973 | MR

[10] Petrovskii I. G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Izd-vo MGU, M., 1984 | MR

[11] Tamura I., Topologiya sloenii, Nauka, M., 1979

[12] Novikov S. P., “Topologiya sloenii”, Tr. Moskovsk. matem. ob-va, 14, no. 2, 1965, 248–278 | MR | Zbl

[13] Gorbuzov V. N., Tyschenko V. Yu., “Chastnye integraly sistem v polnykh differentsialakh”, Differents. uravneniya, 27:10 (1991), 1819–1822 | MR | Zbl

[14] Amelkin V. V., Tyschenko V. Yu., “O suschestvovanii izolirovannykh integralnykh torov differentsialnykh sistem”, Differents. uravneniya, 55:6 (2019), 761–768 | Zbl

[15] Arbuzov A. S., Tyschenko V. Yu., “Priznaki ogranichennosti chisla kompaktnykh invariantnykh giperpoverkhnostei kompleksnykh differentsialnykh sistem”, Vesnik Grodzenskaga DzU. Ser. 2, 2018, no. 1, 6–17