Abstract
AbstractWe construct a large family of Hamiltonian systems which are connected with root systems of complex simple Lie algebras. These systems are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka–Volterra system. We classify all possible Lotka–Volterra systems that arise via this algorithm in the A n case.KeywordsLotka-Volterra SystemHamiltonian Vector FieldCasimirsSimple RootsWell-known Integrable SystemsThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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