119899, Moscow, Vorobyevy gory
M.V.Lomonosov Moscow State University
Veselov A. P., Penskoi A. V.
On algebro-geometric Poisson brakets for the Volterra lattice
1998, vol. 3, no. 2, pp. 3-9
A generalization of the theory of algebro-geometric Poisson brackets on the space of finite-gap Schrodinger operators, developped by S.P.Novikov and A.P.Veselov, to the case of periodic zero-diagonal difference operators of second order is proposed. A necessary and sufficient condition for such a bracket to be compatible with higher Volterra flows is found.
Penskoi A. V.
The Volterra lattice as a gradient flow
1998, vol. 3, no. 1, pp. 76-77
The Volterra latice is considered. New gradient interpretation for this dynamical system is proposed. This interpretation seems to be more natural than existing ones.