Integrable systems and the topology of isospectral manifolds
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 140-146
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We briefly review known results concerning the study of isospectral manifolds using integrable systems. We then describe new results concerning the topology of isospectral manifolds of zero-diagonal Jacobi matrices. This topology is studied using the Volterra system.
Keywords: integrable system, isospectral manifold
Mots-clés : Volterra system.
@article{TMF_2008_155_1_a11,
     author = {A. V. Penskoi},
     title = {Integrable systems and the topology of isospectral manifolds},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {140--146},
     year = {2008},
     volume = {155},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a11/}
}
TY  - JOUR
AU  - A. V. Penskoi
TI  - Integrable systems and the topology of isospectral manifolds
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 140
EP  - 146
VL  - 155
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a11/
LA  - ru
ID  - TMF_2008_155_1_a11
ER  - 
%0 Journal Article
%A A. V. Penskoi
%T Integrable systems and the topology of isospectral manifolds
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 140-146
%V 155
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a11/
%G ru
%F TMF_2008_155_1_a11
A. V. Penskoi. Integrable systems and the topology of isospectral manifolds. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 140-146. http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a11/

[1] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989 | MR | Zbl

[2] C. Tomei, Duke Math. J., 51:4 (1984), 981–996 | DOI | MR | Zbl

[3] R. L. Grekhem, D. Knut, O. Patashnik, Konkretnaya matematika: Osnovanie informatiki, Mir, M., 1998 | MR

[4] D. Fried, Proc. Amer. Math. Soc., 98:2 (1986), 363–368 | DOI | MR | Zbl

[5] A. V. Penskoi, UMN, 62:3 (2007), 213–214 ; arXiv: math-ph/0701061 | DOI | MR | Zbl

[6] S. V. Manakov, ZhETF, 67:2 (1974), 543–555 | MR

[7] M. Kac, P. van Moerbeke, Adv. Math., 16:2 (1975), 160–169 | DOI | MR | Zbl

[8] L. D. Faddeev, L. A. Takhtadzhyan, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[9] A. P. Veselov, A. V. Penskoi, Dokl. RAN, 366:3 (1999), 299–303 | MR | Zbl

[10] P. A. Damianou, Phys. Lett. A, 155:2–3 (1991), 126–132 | DOI | MR

[11] V. L. Vereschagin, Matem. zametki, 48:2 (1990), 145–148 | MR | Zbl

[12] A. M. Bloch, R. W. Brockett, T. S. Ratiu, Comm. Math. Phys., 147 (1992), 57–74 | DOI | MR | Zbl

[13] A. V. Penskoï, Regul. Chaotic Dyn., 3:1 (1998), 76–77 | DOI | MR | Zbl