Kahan discretizations of skew-symmetric Lotka-Volterra systems and Poisson maps (Q2239056)

The primary result of this paper is a characterization of connected, skew-symmetric graphs \(\Gamma\) with the Kahan-Poisson property. The authors show that a graph as such is a cloning of a graph with vertices \(1,2,\ldots,n\), with an arc \(i \to j\) precisely when \(i<j\), and with all arks having the same value. This characterization helps to understand better the integrability of Lotka-Volterra systems as well as their deformations.