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Kowalewski’s asymptotic method, Kac-Moody Lie algebras and regularization. (English) Zbl 0491.58017

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
17B65 Infinite-dimensional Lie (super)algebras
14K99 Abelian varieties and schemes
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[1] Adler, M., van Moerbeke, P.: Completely integrable systems, Euclidean Lie algebras, and curves. Adv. Math.38, 267–317 (1980) · Zbl 0455.58017
[2] Adler, M., van Moerbeke, P.: Linearization of Hamiltonian systems, Jacobi varieties and representation theory. Adv. Math.38, 318–379 (1980) · Zbl 0455.58010
[3] Carter, R.W.: Simple groups of Lie type. London, New York: Wiley 1972 · Zbl 0248.20015
[4] Helgason, S.: Differential geometry, Lie groups and symmetric spaces. New York: Academic Press 1978 · Zbl 0451.53038
[5] Hille, E.: Ordinary differential equations in the complex domain. New York: Wiley-Interscience 1976 · Zbl 0343.34007
[6] Humphreys, J.E.: Introduction to Lie algebras and representation theory. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0254.17004
[7] Kowalewski, S.: Sur le probleme de la rotation d’un corps solide autour d’un point fixe. Acta Math.12, 177–232 (1889) · JFM 21.0935.01
[8] Kowalewski, S.: Sur une propriété du système d’équations différentielles qui définit la rotation d’un corps solide autour d’un point fixe. Acta Math.14, 81–93 (1891) · JFM 22.0921.02
[9] McKean, H.P.: Theta functions, solitons and singular curves, partial differential equations and geometry, pp. 237–254. New York: M. Dekker, Inc. 1979
[10] Bogoyavlensky, O.I.: On perturbations of the periodic Toda lattices. Commun. Math. Phys.51, 201–209 (1976)
[11] Shankar, R.: A model that acquires integrability andO(2N) invariance at a critical coupling. Preprint Yale University YTP 81-06
[12] Adler, M., van Moerbeke, P.: The algebraic integrability of geodesic flow on SO(4). Invent. Math. (to appear) (1982) · Zbl 0539.58012
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