On generalized Volterra systems

2013/05/31 by Charalambides, Stelios A., Damianou, Pantelis A., Evripidou, Charalampos A.
#17B80 (Secondary) #37J35 (Primary) #70H06 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1305.7329

Abstract

We construct a large family of evidently integrable Hamiltonian systems which 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 present in detail all such systems in dimensions 4 and 5 and we also give some examples from higher dimensions. This construction generalizes easily to each complex simple Lie algebra.

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