Geodesic
Canonically conjugate variables for the Volterra lattice with periodic boundary conditions
Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 115-128

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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. 
@article{MZM_1998_64_1_a11,
     author = {A. V. Penskoi},
     title = {Canonically conjugate variables for the {Volterra} lattice with periodic boundary conditions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {115--128},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a11/}
}
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A. V. Penskoi. Canonically conjugate variables for the Volterra lattice with periodic boundary conditions. Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 115-128. http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a11/