13 citations · 13 across the 2 of their papers we have counts for
6 papers
Deducing properties of ODEs from their discretization
G. R. W. Quispel, D. I. McLaren, C. Evripidou
We show that some hard to detect properties of quadratic ODEs (eg certain preserved integrals and measures) can be deduced more or less algorithmically from their Kahan discretizat…
A novel 8-parameter integrable map in
G R W Quispel, D I McLaren, P H van der Kamp
We present a novel 8-parameter integrable map in . The map is measure-preserving and possesses two functionally independent 2-integrals, as well as a measure-preservi…
Homogeneous Darboux polynomials and generalising integrable ODE systems
Peter H. van der Kamp, D. I. McLaren, G. R. W. Quispel
We show that any system of ODEs can be modified whilst preserving its homogeneous Darboux polynomials. We employ the result to generalise a hierarchy of integrable Lotka-Volterra s…
Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
E Celledoni, C Evripidou, D I McLaren +4
In this Letter we propose a systematic approach for detecting and calculating preserved measures and integrals of a rational map. The approach is based on the use of cofactors and…
Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation
Peter H. van der Kamp, Elena Celledoni, Robert I. McLachlan +3
We apply Kahan's discretisation method to three classes of 2-dimensional quadratic vector fields with quadratic, resp cubic, resp quartic Hamiltonians. We show that the maps obtain…
Generalised Manin transformations and QRT maps
Peter H. van der Kamp, David I. McLaren, G. R. W. Quispel
Manin transformations are maps of the plane that preserve a pencil of cubic curves. They are the composition of two involutions. Each involution is constructed in terms of an invol…