Adler, M.; Van Moerbeke, P. Completely integrable systems, Euclidean Lie algebras, and curves. (English) Zbl 0455.58017 Adv. Math. 38, 267-317 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 134 Documents 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 53D50 Geometric quantization 70H05 Hamilton’s equations 70H99 Hamiltonian and Lagrangian mechanics 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B99 Lie algebras and Lie superalgebras 14H40 Jacobians, Prym varieties Keywords:complete integrability of mechanical systems; Hamiltonian systems on the co-adjoint orbit of a solvable group with the Kostant-Kirilov orbit structure; periodic Toda systems; Jacobian of a curve; Toda systems associated to the simple Lie algebras; harmonic oscillators; geodesic flow on an ellipsoid Citations:Zbl 0393.35058; Zbl 0433.22008; Zbl 0361.15010 PDFBibTeX XMLCite \textit{M. Adler} and \textit{P. Van Moerbeke}, Adv. Math. 38, 267--317 (1980; Zbl 0455.58017) Full Text: DOI References: [1] Arnold, V. I., Mathematical Methods of Classical Mechanics (1978), Springer-Verlag: Springer-Verlag New York · Zbl 0386.70001 [2] Kazhdan, D.; Kostant, B.; Sternberg, S., Hamiltonian Group Actions and Dynamical Systems of Calogero Type (July 1978), CPAM [3] van Moerbeke, P.; Mumford, D., The spectrum of difference operators and algebraic curves, Acta Math. (1979) · Zbl 0502.58032 [4] Russian Math. Surveys, 31, No. 1 (1976) [5] Adler, M., On a trace functional for pseudo-differential operators and the symplectic structure of the Korteweg-deVries Equation, Invent. Math., 50, No. 3 (1979) · Zbl 0393.35058 [6] van Moerbeke, P., The spectrum of Jacobi matrices, Invent. Math., 37 (1976) · Zbl 0361.15010 [7] J. Moser; J. 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Math., 59, No. 2, 119-144 (1980) · Zbl 0431.53003 [31] Frenkel, I.; Reiman, A.; Semenov-Tian-Shansky, M., Graded Lie algebras and completely integrable dynamical systems, Soviet Math. Dokl., 20, No. 4, 811-814 (1979) · Zbl 0437.58008 [32] Reiman, A.; Semenov-Tian-Shansky, M., Reduction of Hamiltonian systems, affine Lie algebras and Lax equations, Invent. Math., 54, No. 1, 81-101 (1979) · Zbl 0403.58004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.