105 citations · 316 across the 12 of their papers we have counts for
4 papers · 1 filter
On natural Poisson bivectors on the sphere
A V Tsiganov
We discuss the concept of natural Poisson bivectors, which allows us to consider the overwhelming majority of known integrable systems on the sphere in framework of bi-Hamiltonian…
On bi-integrable natural Hamiltonian systems on the Riemannian manifolds
A. V. Tsiganov
We introduce the concept of natural Poisson bivectors, which generalizes the Benenti approach to construction of natural integrable systems on the Riemannian manifolds and allows u…
Integrable Euler top and nonholonomic Chaplygin ball
A V Tsiganov
We discuss the Poisson structures, Lax matrices, -matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems…
New variables of separation for particular case of the Kowalevski top
A V Tsiganov
We discuss the polynomial bi-Hamiltonian structures for the Kowalevski top in special case of zero square integral. An explicit procedure to find variables of separation and separa…