Regular and Chaotic Dynamics

, Volume 13, Issue 6, pp 543–556 | Cite as

Integrable Lotka-Volterra systems

Jürgen Moser - 80

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 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada
  2. 2.V.A. Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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