Multi-Hamiltonian structures for r-matrix systems

Details Multi-Hamiltonian structures for r-matrix systems Multi-Hamiltonian structures for r-matrix systems

2002-11-29

arxiv.org/abs/math-ph/0211076v1

J.Math.Phys.49:062903,2008

Physics

Mathematical Physics

26 pages, Plain Tex

Scientific paper

10.1063/1.2937896

For the rational, elliptic and trigonometric r-matrices, we exhibit the links between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral curves and sheaves supported on them; (c) Symmetric products of a surface. We have, at each level, a linear space of compatible Poisson structures, and the maps relating the levels are Poisson. This leads in a natural way to Nijenhuis coordinates for these spaces. At level (b), there are Hamiltonian systems on these spaces which are integrable for each Poisson structure in the family, and which are such that the Lagrangian leaves are the intersections of the symplective leaves over the Poisson structures in the family. Specific examples include many of the well-known integrable systems.

Affiliated with

Also associated with

No associations

Rating

Multi-Hamiltonian structures for r-matrix systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multi-Hamiltonian structures for r-matrix systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multi-Hamiltonian structures for r-matrix systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-91881