Adler, M.; van Moerbeke, P. Kowalewski’s asymptotic method, Kac-Moody Lie algebras and regularization. (English) Zbl 0491.58017 Commun. Math. Phys. 83, 83-106 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 43 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 17B65 Infinite-dimensional Lie (super)algebras 14K99 Abelian varieties and schemes Keywords:asymptotic analysis of Hamiltonian vector fields; linearizable Hamiltonian vector fields on abelian varieties; interactions; Toda systems for the Kac-Moody Lie algebras PDFBibTeX XMLCite \textit{M. Adler} and \textit{P. van Moerbeke}, Commun. Math. Phys. 83, 83--106 (1982; Zbl 0491.58017) Full Text: DOI References: [1] Adler, M., van Moerbeke, P.: Completely integrable systems, Euclidean Lie algebras, and curves. Adv. Math.38, 267–317 (1980) · Zbl 0455.58017 · doi:10.1016/0001-8708(80)90007-9 [2] Adler, M., van Moerbeke, P.: Linearization of Hamiltonian systems, Jacobi varieties and representation theory. Adv. Math.38, 318–379 (1980) · Zbl 0455.58010 · doi:10.1016/0001-8708(80)90008-0 [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 · doi:10.1007/BF02592182 [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 · doi:10.1007/BF02413316 [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) · doi:10.1007/BF01617919 [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 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.