Symplectic leaves of the Gel'fand--Dikii brackets and homotopy classes of nondegenerate curves

V. Yu. Ovsienko ; B. A. Khesin

Funkcionalʹnyj analiz i ego priloženiâ, Tome 24 (1990) no. 1, pp. 38-47.

Bibliographie

[1] Gelfand I.M., Dikii L.A., “Drobnye stepeni operatorov i gamiltonovy sistemy”, Funktsion. analiz i ego pril., 10:4 (1976), 13–29 | MR | Zbl

[2] Gelfand I.M., Dikii L.A., Semeistvo gamiltonovykh struktur, svyazannykh s nelineinymi integriruemymi uravneniyami, Preprint IPM, no. 136, 1978

[3] Little J.A., “Nondegenerate homotopics of curves on the unite 2-ephere”, J. Diff. Geom., 4:3 (1970), 339–348 | MR | Zbl

[4] Shapiro B.Z., Shapiro M.Z., “On the number connected components in the space of closed nondegenerate curves on $S^n$”, Submitted to Bull. Amer. Math. Soc., 1984 | MR

[5] Kuiper N.H., “Locally projective spaces of dimension one”, Michigan Math. J., 2:2 (1954), 95–97 | MR

[6] Lazutkin V.F., Pankratova T.F., “Normalnye formy i versalnye deformatsii dlya uravnenii Khilla”, Funktsion. analiz i ego pril., 9:4 (1975), 41–48 | MR | Zbl

[7] Kirillov A.A., “Infinite dimensional Lie groups: their orbits, invariants and representations. Geometry of moments”, Lect Notes in Math., no. 970, 1982, 101–123 | DOI | MR | Zbl

[8] Segal G., “Unitary representations of some infinite dimensional groups”, Comm. Math. Phys., 80:3 (1981), 301–342 | DOI | MR | Zbl

[9] Ovsienko V.Yu., “Klassifikatsiya lineinykh differentsialnykh uravnenii tretego poryadka i simplekticheskikh listov skobki Gelfanda–Dikogo”, Mat. zametki, 47:5 (1990), 62–70 | MR | Zbl

[10] Ovsienko V.Yu., Ovsienko O.D., Chekanov Yu.V., “Klassifikatsiya kontaktno-proektivnykh struktur na superokruzhnosti”, UMN, 44:3 (1989), 167–168 | MR

[11] Khesin B.A., “Invarianty gamiltonovykh KdV-struktur”, UMN, 45:1 (1990), 195–196 | MR | Zbl

[12] Zamolodchikov A.B., “Dopolnitelnye simmetrii v dvumernoi kvantovoi konformnoi teorii polya”, TMF, 65:3 (1985), 347–359 | MR

[13] Lukyanov S.L., “Kvantovanie skobki Gelfanda–Dikogo”, Funktsion. analiz i ego pril., 22:4 (1988), 1–10 | MR

[14] Witten E., “Coadjoint Orbits of the Virasoro Group”, Comm. Math. Phys., 114:1 (1988), 1–53 | DOI | MR | Zbl

[15] Drinfeld B.G., Sokolov V.V., “Algebry Li i uravneniya tipa Kortvega–de Friza”, Itogi nauki i tekhniki SSSR. Sovremennye problemy matematiki, 24, 1984, 81–180 | MR

[16] Arnold V.I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

[17] Khovanova T.G., “Algebry Li Gelfanda–Dikogo i algebra Virasoro”, Funktsion. analiz i ego pril., 20:4 (1986), 89–90 | MR | Zbl

[18] Hartman P., “On nonoscillatory linear differential equations Avith monotonie coefficients”, Amer. Math. J., 76 (1954), 207–219 | DOI | MR | Zbl

[19] Vershik A.M., Gershkovich V.Ya., “Negolonomnye dinamicheskie sistemy. Geometriya raspredelenii i variatsionnye zadachi”, Itogi nauki i tekhniki SSSR. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 16, 1987, 5–85 | MR | Zbl

[20] Hamenstddt U., “Zur Theorie von Carnot–Caratheodory Metriken und ihren Anwendungen”, Bonn. Math. Schr., 1987, no. 180, 1–64 | MR

[21] Khovanova T.G., “Struktura superalgebry Li na sobstvennykh funktsiyakh i struyakh yadra rezolventy vblizi diagonali dlya differentsialnykh operatorov $n$-go poryadka”, Funktsion. analiz i ego pril., 20:2 (1986), 88–89 | MR | Zbl

[22] Shapiro B.Z., Shapiro M.Z., Khenn B.A., “On the number of connected components of nondegenerate curves on $S^2$ with given monodromy”, Submitted to J. Diff. Geom., 1986 | MR