@article{CM_1993__87_2_153_0, author = {Audin, Michele and Silhol, Robert}, title = {Vari\'et\'es ab\'eliennes r\'eelles et toupie de {Kowalevski}}, journal = {Compositio Mathematica}, pages = {153--229}, publisher = {Kluwer Academic Publishers}, volume = {87}, number = {2}, year = {1993}, mrnumber = {1219634}, zbl = {0774.58012}, language = {fr}, url = {http://archive.numdam.org/item/CM_1993__87_2_153_0/} }
TY - JOUR AU - Audin, Michele AU - Silhol, Robert TI - Variétés abéliennes réelles et toupie de Kowalevski JO - Compositio Mathematica PY - 1993 SP - 153 EP - 229 VL - 87 IS - 2 PB - Kluwer Academic Publishers UR - http://archive.numdam.org/item/CM_1993__87_2_153_0/ LA - fr ID - CM_1993__87_2_153_0 ER -
Audin, Michele; Silhol, Robert. Variétés abéliennes réelles et toupie de Kowalevski. Compositio Mathematica, Volume 87 (1993) no. 2, pp. 153-229. http://archive.numdam.org/item/CM_1993__87_2_153_0/
[1] 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. | MR | Zbl
, :[2] 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. | MR | Zbl
and[3] Traité de mécanique rationnelle, vol. II, Gauthier-Villars, Paris, 1931.
:[4] Non Totally Symmetric Gyroscopes, Moscow 1940.
,[5] Méthodes Mathématiques de la Mécanique Classique, MIR, Moscou, 1974. | Zbl
:[6] The Topology of Torus Actions on Symplectic Manifolds, Progress in Math. 93, Birkhäuser, 1991. | MR | Zbl
:[7] The Kowalevski top 99 years later: A Lax pair, generalizations and explicit solutions, Commun. Math. Phys. 122 (1989), 321-354. | MR | Zbl
, , :[8] Sulle varietà abeliane reale I e II, Ann. Mat. Puro Appl. 2 (1924), 67-106 et 4 (1926), 27-71. | JFM
:[9] Riemann Surfaces, Graduate texts in Math. 71, Springer, 1980. | MR | Zbl
and :[10] Theta functions on Riemann surfaces, Lecture Notes in Mathematics, Springer, 392, 1973. | MR | Zbl
:[11] The topology of surfaces of constant energy in integrable hamiltonian systems and obstructions to integrability, Math. USSR Izvestya 29 (1987), 629-658. | Zbl
:[12] Integrability and Nonintegrability in Geometry and Mechanics, Math. and its Applications, Kluwer, 1988. | MR | Zbl
:[13] Real abelian varieties and the singularities of an integrable hamiltonian system, Real analytic and algebraic geometry, Lecture Notes in Mathematics, 1420, 1990. | Zbl
and :[14] Lectures on Integration of the Equations of Motion of a Rigid Body about a Fixed Point, Israel program for scientific translations, Haifa, 1960. | MR | Zbl
:[15] Linearizing flows and a cohomological interpretation of Lax equations, Amer. J. Math. 107 (1985), 1445-1483. | MR | Zbl
:[16] Real algebraic curves, Ann. Sci. Ec. Norm. Sup. 14 (1981), 157-182. | EuDML | Numdam | MR | Zbl
and :[17] Geodesic flow on SO(4) and abelian surfaces, Math. Ann. 263 (1983), 435-472. | EuDML | MR | Zbl
:[18] The full geometry of Kowalevski's top and (1, 2)-abelian surfaces, Comm. Pure and Appl. Math. 42 (1989), 357-407. | MR | Zbl
and :[19] Bifurcation of common levels of first integrals of the Kowalevskaya problem, PMN U.S.S.R. 47 (1983), 737-743. | MR | Zbl
:[20] Sur le problème de la rotation d'un corps solide autour d'un point fixe, Acta Math. 12 (1889), 177-232. | JFM
:[21] Note on the integration of Euler's equations of the dynamics of an n-dimensional rigid body, Funct. Anal. Appl. 11 (1976), 328-329. | Zbl
:[22] P. van Moerbeke: The Lagrange rigid body motion, Ann. Institut Fourier 33 (1982), 211-234. | EuDML | Numdam | MR | Zbl
and[23] Integrable hamiltonian systems connected with graded Lie algebras, J. Soviet Math. 19 (1982), 1507-1545. | Zbl
:[24] Moduli spaces for real algebraic curves and real abelian varieties, Math. Z. 201 (1989), 151-165. | EuDML | MR | Zbl
and :[25] Groupes Algébriques et Corps de Classes, Hermann, Paris, 1959. | Zbl
:[26] Real algebraic surfaces, Lecture Notes in Mathematics, Springer, 1392, 1989. | MR | Zbl
:[27] Compactifications of real moduli spaces in real algebraic geometry, Invent. Math. 107 (1992), 151-202. | EuDML | MR | Zbl
:[28] Algèbres de Lie, systèmes hamiltoniens, courbes algébriques, Séminaire Bourbaki, Springer (1980), 85-94. | EuDML | Numdam | MR | Zbl
:[29] Euler and the Jacobians of elliptic curves, arithmetic and geometry, papers dedicated to Shafarevich, Progress in Math., Birkhäuser, 1983. | MR | Zbl
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