Jürgen Moser - 80

Regular and Chaotic Dynamics

, Volume 13, Issue 6, pp 543-556

Integrable Lotka-Volterra systems

  • O. I. BogoyavlenskijAffiliated withDepartment of Mathematics, Queen’s UniversityV.A. Steklov Institute of Mathematics, Russian Academy of Sciences Email author 

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Abstract

Infinite- and finite-dimensional lattices of Lotka-Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka- Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions.

Key words

Lax representation Hamiltonian structures Casimir functions Riemannian surfaces Lotka-Volterra systems integrable lattices

MSC2000 numbers

58F05