303 citations · 399 across the 20 of their papers we have counts for
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Trees and superintegrable Lotka-Volterra families
Peter H. van der Kamp, G. R. W. Quispel, D. I. McLaren
To any tree on vertices we associate an -dimensional Lotka-Volterra system with parameters and, for generic values of the parameters, prove it is superintegrable, i.e…
Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation
Peter H. van der Kamp, Robert I. McLachlan, David I. McLaren +1
We show that any Lotka--Volterra tree-system associated with an -vertex tree, as introduced in Quispel et al., J. Phys. A 56 (2023) 315201, preserves a rational measure. We also…
Birational maps from polarization and the preservation of measure and integrals
Robert I McLachlan, David I McLaren, G R W Quispel
The main result of this paper is the discretization of Hamiltonian systems of the form , where is a constant symmetric matrix and $W\colon\mathbb{R}^n…
Linear Darboux polynomials for Lotka-Volterra systems, trees and superintegrable families
G. R. W. Quispel, Benjamin K. Tapley, D. I. McLaren +1
We present a method to construct superintegrable -component Lotka-Volterra systems with parameters. We apply the method to Lotka-Volterra systems with components for…