Abstract
We use an effective criterion based on the asymptotic analysis of a class of Hamiltonian equations to determine whether they are linearizable on an abelian variety, i.e., solvable by quadrature. The criterion is applied to a system with Hamiltonian
parametrized by a real matrixN=(N ij ) of full rank. It will be solvable by quadrature if and only if for alli≠j, 2(N NT) ij (N N T) −1 jj is a nonpositive integer, i.e., the interactions correspond to the Toda systems for the Kac-Moody Lie algebras. The criterion is also applied to a system of Gross-Neveu.
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Communicated by J. Moser
Supported in part by NSF contract MCS 79-17385
Supported in part by NSF contract MCS 79-05576
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Adler, M., van Moerbeke, P. Kowalewski's asymptotic method, Kac-Moody lie algebras and regularization. Commun.Math. Phys. 83, 83–106 (1982). https://doi.org/10.1007/BF01947073
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DOI: https://doi.org/10.1007/BF01947073