Multi-Hamiltonian property of a~linear system with quadratic invariant
Algebra i analiz, Tome 30 (2018) no. 5, pp. 159-168.

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

@article{AA_2018_30_5_a5,
     author = {V. V. Kozlov},
     title = {Multi-Hamiltonian property of a~linear system with quadratic invariant},
     journal = {Algebra i analiz},
     pages = {159--168},
     publisher = {mathdoc},
     volume = {30},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2018_30_5_a5/}
}
TY  - JOUR
AU  - V. V. Kozlov
TI  - Multi-Hamiltonian property of a~linear system with quadratic invariant
JO  - Algebra i analiz
PY  - 2018
SP  - 159
EP  - 168
VL  - 30
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2018_30_5_a5/
LA  - ru
ID  - AA_2018_30_5_a5
ER  - 
%0 Journal Article
%A V. V. Kozlov
%T Multi-Hamiltonian property of a~linear system with quadratic invariant
%J Algebra i analiz
%D 2018
%P 159-168
%V 30
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2018_30_5_a5/
%G ru
%F AA_2018_30_5_a5
V. V. Kozlov. Multi-Hamiltonian property of a~linear system with quadratic invariant. Algebra i analiz, Tome 30 (2018) no. 5, pp. 159-168. http://geodesic.mathdoc.fr/item/AA_2018_30_5_a5/

[1] Kozlov V V., “Lineinye sistemy s kvadratichnym integralom”, Prikl. mat. mekh., 56:6 (1992), 900–906 | MR | Zbl

[2] Treschev D. V., Shkalikov A. A., “O gamiltonovosti lineinykh dinamicheskikh sistem v gilbertovom prostranstve”, Mat. zametki, 101:6 (2017), 911–918 | DOI | MR

[3] Volterra V., “Sopra una classe di equazioni dinamiche”, Atti Accad. Sci. Torino, 33 (1897–98), 451–475

[4] Gledzer E. B., Dolzhanskii F. V., Obukhov A. M., Sistemy gidrodinamicheskogo tipa i ikh primenenie, Nauka, M., 1981 | MR

[5] Bizyaev I. A., Kozlov V. V., “Odnorodnye sistemy s kvadratichnymi integralami, kvaziskobki Li–Puassona i metod Kovalevskoi”, Mat. sb., 206:12 (2015), 29–54 | DOI | MR | Zbl

[6] Kozlov V. V., “Linear Hamiltonian systems: quadratic integrals, singular subspaces and stability”, Regul. Chaotic Dyn., 23:1 (2018), 26–46 | DOI | MR

[7] Williamson J., “An algebraic problem involving the involutory integrals of linear dynamical systems”, Amer. J. Math., 62 (1940), 881–911 | DOI | MR | Zbl | Zbl

[8] Magri F., “A simple model of the integrable Hamiltonian equation”, J. Math. Phys., 19:5 (1978), 1156–1162 | DOI | MR | Zbl

[9] Olver P., Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989

[10] Borisov A. V., Mamaev I. S., Sovremennye metody teorii integriruemykh sistem, Inst. kompyut. issled., Moskva–Izhevsk, 2003

[11] Wintner A., “On the linear conservative dynamical systems”, Ann. Mat. Pura Appl., 13:1 (1934), 105–112 | DOI | MR | Zbl

[12] Koçak H., “Linear Hamiltonian systems are integrable with quadratics”, J. Math. Phys., 23:12 (1982), 2375–2380 | DOI | MR

[13] Kozlov V. V., “O mekhanizme poteri ustoichivosti”, Differents. uravn., 45:4 (2009), 496–505 | MR | Zbl

[14] Veil G., Klassicheskie gruppy, ikh invarianty i predstavleniya, IL, M., 1947

[15] Kozlov V. V., “Liuvillevost invariantnykh mer vpolne integriruemykh sistem i uravnenie Monzha–Ampera”, Mat. zametki, 53:4 (1993), 45–52 | MR | Zbl