Geodesic
Integrable systems and the topology of isospectral manifolds
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 140-146

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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. 
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/
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[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