Abstract
The Volterra lattice is considered. This dynamical system is known to be Hamiltonian with respect to two compatible Poisson brackets (quadratic and cubic). For each of the two brackets, a set of canonically conjugate variables is found by using the spectral theory of the Jacobi operator.
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Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 115–128, July, 1998.
The author wishes to express his gratitude to A. P. Veselov for setting the problem and for useful discussions.
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Penskoi, A.V. Canonically conjugate variables for the Volterra lattice with periodic boundary conditions. Math Notes 64, 98–109 (1998). https://doi.org/10.1007/BF02307200
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DOI: https://doi.org/10.1007/BF02307200