53 citations · 187 across the 29 of their papers we have counts for
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Poisson structures for difference equations
Charalampos A. Evripidou, G. R. W. Quispel, John A. G. Roberts
We study the existence of log-canonical Poisson structures that are preserved by difference equations of special form. We also study the inverse problem, given a log-canonical Pois…
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…
Geometric and integrability properties of Kahan's method
Elena Celledoni, David McLaren, Brynjulf Owren +1
Given a quadratic vector field on \mathbb{R}^n possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discre…