Variétés abéliennes réelles et toupie de Kowalevski

Michele Audin; Robert Silhol

Compositio Mathematica (1993)

  • Volume: 87, Issue: 2, page 153-229
  • ISSN: 0010-437X

How to cite


Audin, Michele, and Silhol, Robert. "Variétés abéliennes réelles et toupie de Kowalevski." Compositio Mathematica 87.2 (1993): 153-229. <>.

author = {Audin, Michele, Silhol, Robert},
journal = {Compositio Mathematica},
keywords = {spectral curve; Liouville tori},
language = {fre},
number = {2},
pages = {153-229},
publisher = {Kluwer Academic Publishers},
title = {Variétés abéliennes réelles et toupie de Kowalevski},
url = {},
volume = {87},
year = {1993},

AU - Audin, Michele
AU - Silhol, Robert
TI - Variétés abéliennes réelles et toupie de Kowalevski
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 87
IS - 2
SP - 153
EP - 229
LA - fre
KW - spectral curve; Liouville tori
UR -
ER -


  1. [1] M. Adler, P. van Moerbeke: Completely integrable systems, euclidian Lie algebras and curves, et Linearization of hamiltonian systems, Jacobi varieties and representation theory, Advances in Math.38 (1980), 267-317 et 318-379. Zbl0455.58010MR597730
  2. [2] M. Adler and P. van Moerbeke: The Kowalevski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs, Comm. Math. Phys.113 (1988), 659-700. Zbl0647.58022MR923636
  3. [3] P. Appell: Traité de mécanique rationnelle, vol. II, Gauthier-Villars, Paris, 1931. 
  4. [4] G.G. Appelrot, Non Totally Symmetric Gyroscopes, Moscow1940. 
  5. [5] V.I. Arnold: Méthodes Mathématiques de la Mécanique Classique, MIR, Moscou, 1974. Zbl0385.70001
  6. [6] M. Audin: The Topology of Torus Actions on Symplectic Manifolds, Progress in Math.93, Birkhäuser, 1991. Zbl0726.57029MR1106194
  7. [7] A.I. Bobenko, A.G. Reyman, M.A. Semenov-Tian-Shansky: The Kowalevski top 99 years later: A Lax pair, generalizations and explicit solutions, Commun. Math. Phys.122 (1989), 321-354. Zbl0819.58013MR994508
  8. [8] A. Comessatti: Sulle varietà abeliane reale I e II, Ann. Mat. Puro Appl.2 (1924), 67-106 et 4 (1926), 27-71. Zbl50.0641.01JFM51.0294.02
  9. [9] H. Farkas and I. Kra: Riemann Surfaces, Graduate texts in Math.71, Springer, 1980. Zbl0475.30001MR583745
  10. [10] J.D. Fay: Theta functions on Riemann surfaces, Lecture Notes in Mathematics, Springer, 392, 1973. Zbl0281.30013MR335789
  11. [11] A.T. Fomenko: The topology of surfaces of constant energy in integrable hamiltonian systems and obstructions to integrability, Math. USSR Izvestya29 (1987), 629-658. Zbl0649.58019
  12. [12] A.T. Fomenko: Integrability and Nonintegrability in Geometry and Mechanics, Math. and its Applications, Kluwer, 1988. Zbl0675.58018MR973403
  13. [13] J.-P. Françoise and R. Silhol: Real abelian varieties and the singularities of an integrable hamiltonian system, Real analytic and algebraic geometry, Lecture Notes in Mathematics, 1420, 1990. Zbl0697.58024
  14. [14] V.V. Golubev: Lectures on Integration of the Equations of Motion of a Rigid Body about a Fixed Point, Israel program for scientific translations, Haifa, 1960. Zbl0122.18701MR116511
  15. [15] P.A. Griffiths: Linearizing flows and a cohomological interpretation of Lax equations, Amer. J. Math.107 (1985), 1445-1483. Zbl0585.58028MR815768
  16. [16] B. Gross and J. Harris: Real algebraic curves, Ann. Sci. Ec. Norm. Sup.14 (1981), 157-182. Zbl0533.14011MR631748
  17. [17] L. Haine: Geodesic flow on SO(4) and abelian surfaces, Math. Ann.263 (1983), 435-472. Zbl0521.58042MR707241
  18. [18] E. Horozov and P. van Moerbeke: The full geometry of Kowalevski's top and (1, 2)-abelian surfaces, Comm. Pure and Appl. Math.42 (1989), 357-407. Zbl0689.58020MR990136
  19. [19] M.P. Kharlamov: Bifurcation of common levels of first integrals of the Kowalevskaya problem, PMN U.S.S.R.47 (1983), 737-743. Zbl0579.70003MR786376
  20. [20] S. Kowalevski: Sur le problème de la rotation d'un corps solide autour d'un point fixe, Acta Math.12 (1889), 177-232. JFM21.0935.01
  21. [21] S.V. Manakov: Note on the integration of Euler's equations of the dynamics of an n-dimensional rigid body, Funct. Anal. Appl.11 (1976), 328-329. Zbl0358.70004
  22. [22] T. Ratiu and P. van Moerbeke: The Lagrange rigid body motion, Ann. Institut Fourier33 (1982), 211-234. Zbl0466.58020MR658949
  23. [23] A.G. Reiman: Integrable hamiltonian systems connected with graded Lie algebras, J. Soviet Math.19 (1982), 1507-1545. Zbl0554.70010
  24. [24] M. Seppala and R. Silhol: Moduli spaces for real algebraic curves and real abelian varieties, Math. Z.201 (1989), 151-165. Zbl0645.14012MR997218
  25. [25] J.-P. Serre: Groupes Algébriques et Corps de Classes, Hermann, Paris, 1959. Zbl0097.35604
  26. [26] R. Silhol: Real algebraic surfaces, Lecture Notes in Mathematics, Springer, 1392, 1989. Zbl0691.14010MR1015720
  27. [27] R. Silhol: Compactifications of real moduli spaces in real algebraic geometry, Invent. Math.107 (1992), 151-202. Zbl0777.14014MR1135469
  28. [28] J.-L. Verdier: Algèbres de Lie, systèmes hamiltoniens, courbes algébriques, Séminaire Bourbaki, Springer (1980), 85-94. Zbl0492.58014MR647490
  29. [29] A. Weil: Euler and the Jacobians of elliptic curves, arithmetic and geometry, papers dedicated to Shafarevich, Progress in Math., Birkhäuser, 1983. Zbl0554.01014MR717601

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.