From the Toda Lattice to the Volterra lattice and back

Abstract

We discuss the relationship between the multiple Hamiltonian structures of the generalized Toda lattices and that of the generalized Volterra lattices. We use a symmtery approach for Poisson structures that generalizes the Poisson involution theorem.

arXiv comment15 pages; Final version to appear in Reports on Math. Phys

References in corpus (1)

• Multiple Hamiltonian Structures for Toda-type systems

Cited by in corpus (7)

• Liouville integrability and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization
• Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices
• Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
• Bogoyavlensky--Volterra and Birkhoff Integrable Systems
• Invariant critical sets of conserved quantities
• A symplectic realization of the Volterra lattice
• Reduction and Realization in Toda and Volterra