A Gentle (without Chopping) Approach to the Full Kostant-Toda Lattice

In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant-Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the space of maps from Z_n to GL(n,R) endowed with a structure of a pair of Lie-algebroids.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The modular hierarchy of the Toda lattice

The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of integrable systems. We illustrate in detail the case of the Toda lattice both in Flaschka and natural coordinates.Comment: 16 pages, 29 references, to appear in Differential Geometry and its application