Loughborough, LE11 3TU, UK
Department of Mathematical Sciences, Loughborough University
Veselov A. P.
A few things I learnt from Jürgen Moser
2008, vol. 13, no. 6, pp. 515-524
A few remarks on integrable dynamical systems inspired by discussions with Jürgen Moser and by his work.
Dullin H. R., Richter P. H., Veselov A. P.
Action variables of the Kovalevskaya top
1998, vol. 3, no. 3, pp. 18-31
An explicit formula for the action variables of the Kovalevskaya top as Abelian integrals of the third kind on the Kovalevskaya curve is found. The linear system of differential equations of Picard–Fuchs type, describing the dependence of these variables on the integrals of the Kovalevskaya system, is presented in explicit form. The results are based on the formula for the actions derived by S.P.Novikov and A.P.Veselov within the theory of algebro-geometric Poisson brackets on the universal bundle of hyperelliptic Jacobians.
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.