Variétés abéliennes réelles et toupie de Kowalevski

Michele Audin; Robert Silhol

Compositio Mathematica (1993)

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

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Audin, Michele, and Silhol, Robert. "Variétés abéliennes réelles et toupie de Kowalevski." Compositio Mathematica 87.2 (1993): 153-229. <http://eudml.org/doc/90232>.

@article{Audin1993,
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 = {http://eudml.org/doc/90232},
volume = {87},
year = {1993},
}

TY - JOUR
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 - http://eudml.org/doc/90232
ER -

References

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  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

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