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Completely integrable Hamiltonian systems connected with semisimple Lie algebras. (English) Zbl 0342.58017

##### MSC:
 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 17B80 Applications of Lie algebras and superalgebras to integrable systems 70H05 Hamilton’s equations 70F10 $$n$$-body problems
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##### References:
 [1] Arnold, V.I.: Mathematical methods of classical mechanisms. Moscow, 1974 (in Russian) [2] Moser, J.: Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math.16, 197 (1975). · Zbl 0303.34019 [3] Calogero, F.: Solution of the one-dimensionaln-body problems with quadratic and/or inversly quadratic pair potentials. J. Math. Phys.12, 419-436 (1971) [4] Sutherland, B.: Exact results for a quantum many-body problem in one dimension. II. Phys. Rev.A5, 1372-1376 (1972) [5] Lax, P. D.: Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math.21, 467-490 (1968) · Zbl 0162.41103 [6] Calogero, F., Marchioro C., Ragnisco, O.: Exact solution of the classical and quantal one-dimensional many-body problems with the two-body potentialV ?(x)=g 2 a 2/sinh2 a x. Lett. Nuovo Cim.13, 383-387 (1975) [7] Calogero, F.: Exactly solvable one-dimensional many-body problems. Lett. Nuovo Cim.13, 411-416 (1975) [8] Bourbaki, N.: Groupes et algebras de Lie, Chapitres 4 5 et 6. Paris: Hermann 1969 · Zbl 0205.06001 [9] Olshanetsky, M. A., Perelomov, A. M.: Completely integrable classical systems connected with semisimple Lie algebras. I. Lett. Math. Phys. (1976) · Zbl 0343.70010 [10] Perelomov, A. M.: Completely integrable classical systems connected with semisimple Lie algebras. II. Preprint ITEP No. 27 (1976) · Zbl 0343.70010 [11] Adler, M.: A New Integrable System and a Conjecture by Calogero. Preprint (1975) [12] Bateman, H., Erdélyi, A.: Higher transcendental functions, v. 3, N. Y. 1955 · Zbl 0143.29202
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