Generalized Jacobians of spectral curves and completely integrable systems

Mathematische Zeitschrift

Volumn 230, Issue 3, 1999, Pages 487-508

  Gavrilov, Lubomir ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033416562     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004701     Document Type: Article

References (20)

1. M.R. Adams, J. Harnad, J. Hurtubise, Isospectral Hamiltonian flows in finite and infinite dimension, Commun. Math. Phys. 134, 555-585 (1990).
2. M. Adler, P. van Moerbeke, Linearization of Hamiltonian systems, Jacobi varieties and representation theory, Advances in Math. 38, 318-379 (1980).
3. M. Audin, Spinning Tops, Cambridge Studies in Advanced Mathematics 51, Cambridge University Press. Cambridge, 1996.
4. A. Beauville, Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta Math. 164, 211-235 (1990).
5. E.D. Belokolos, A.I. Bobenko, V.Z. Enol'skii, A.R. Its, V.B. Matveev, Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer, 1994.
6. A. Clebsch, P. Gordan, Theorie der abelschen Functionen, Leipzig, 1866.
7. J.D. Fay, Theta Functions on Riemann Surfaces, Lect. Notes in Mathematics No 352, Springer, 1973.
8. Yu. Fedorov, Integrable systems related to generalized Jacobians, Acta Appl. Math., to appear.
9. L. Gavrilov, A. Zhivkov, The complex geometry of Lagrange top, Einseignement Mathématique, v. 44 (1998) pp. 133-170.
10. C. Jacobi, Über eine neue Methode zur Integration der hyperelliptischen Differentialgleichungen und über die rationale Form ihrer vollständigen algebraischen Integralgleichungen. Crelle, Bd. 32, p. 220-226 (1846).
11. A. Krazer, W. Wirtinger, Abelsche funktionen und allgemeine thetafunktionen, in Enciklopadic der Math. Wiss., Leipzig, 1901-1921, Band 2, Teil 2, pp. 604-873.
12. J.L. Lagrange, Mécanique Analytique, 1788, in Œvres de Lagrange, tome XII, Gauthier-Villars, 1889.
13. P. van Moerbeke, D. Mumford, The spectrum of difference operators and algebraic curves, Acta Math. 143, 93-154 (1979).
14. D. Mumford, Tata Lectures on Theta II, Progress in Mathematics 43, Birkhäuser, 1984.
15. L. Previato, Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation, Duke Math. J. 52, 329-377 (1985).
16. T. Ratiu, P. van Moerbeke. The Lagrange rigid body motion, Ann. Inst. Fourier 32, 211-234 (1982).
17. A.G. Reyman, M.A. Semenov-Tian-Shansky. Group theoretical methods in the theory of finite dimensional Integrable systems, in Dynamical Systems VII, Enciclopaedia of Mathematical Sciences, 16, Springer, 1994.
18. M.A. Semenov-Tian-Shanski, What a classical r-matrix is, Funct. Anal. Appl. 17, 259-272 (1983).
19. J.-P. Serre, Groupes Algébriques et Corps de Classes, Hermann, Paris, 1959.
20. J.-L. Verdier, Algébres de Lie, systèmes Hamiltoniens, courbes algébriques. Séminaire E.N.S. (1979-82) Prog. Math. 37, 237-246 (1983), Birkhauser.