Reduction and Realization in Toda and Volterra

Abstract

We construct a new symplectic, bi-hamiltonian realization of the KM-system by reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper we also review the important work of Moser on the Toda and KM-systems.

17 pages

References in corpus (3)

• Multiple Hamiltonian Structures for Toda-type systems
• From the Toda Lattice to the Volterra lattice and back
• Bogoyavlensky--Volterra and Birkhoff Integrable Systems

Cited by in corpus (2)

• New global solutions of the Jacobi partial differential equations
• Isospectral flows on a class of finite-dimensional Jacobi matrices