Presented by Dr. Charalampos EVRIPIDOU on 22 Jun 2023 from 17:30 to 18:00
Session: Darboux polynomials
The Kahan discretization of a Lotka-Volterra system leads to a rational map parametrized by the step size. When this map is Poisson with respect to the quadratic Poisson structure of the Lotka-Volterra system we say that this system has the Kahan-Poisson property. There is a well known family of Lotka-Volterra systems having the Kahan-Poisson property. Their underlying graph has n vertices 1, 2, ..., n and an arc from i to j precicely when i less than j. We prove that, modulo permutation of the variables and clonings, these are the only Lotka-Volterra systems having the Kahan-Poisson property.