The Banach Poisson geometry of multi-diagonal Toda-like lattices

Details The Banach Poisson geometry of multi-diagonal Toda-like lattices The Banach Poisson geometry of multi-diagonal Toda-like lattices

2003-10-20

arxiv.org/abs/math/0310318v3

Mathematics

Symplectic Geometry

46 pages

Scientific paper

The Banach Poisson geometry of multi-diagonal Hamiltonian systems having infinitely many integrals in involution is studied. It is shown that these systems can be considered as generalizing the semi-infinite Toda lattice which is an example of a bidiagonal system, a case to which special attention is given. The generic coadjoint orbits of the Banach Lie group of bidiagonal bounded operators are studied. It is shown that the infinite dimensional generalization of the Flaschka map is a momentum map. Action-angle variables for the Toda system are constructed.

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