On generalized Volterra systems
Mathematical Physics
2013-06-03 v1 Dynamical Systems
math.MP
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.
Cite
@article{arxiv.1305.7329,
title = {On generalized Volterra systems},
author = {Stelios A. Charalambides and Pantelis A. Damianou and Charalampos A. Evripidou},
journal= {arXiv preprint arXiv:1305.7329},
year = {2013}
}
Comments
26 pages