2,688 research outputs found
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
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
- …