We contribute to the algebraic-geometric study of discrete integrable systems generated by
planar birational maps:(a) we find geometric description of Manin involutions for elliptic …

We apply Kahan's discretisation method to three classes of 2D quadratic vector fields with
quadratic, resp. cubic, resp. quartic Hamiltonians. We show that the maps obtained in this …

We present some new families of quadratic vector fields, not necessarily integrable, for
which their Kahan–Hirota–Kimura discretization exhibits the preservation of some of the …

We determine the affine Weyl symmetries of some two-dimensional birational maps known
as QRT roots arising from Kahan--Hirota--Kimura discretisation of two different reduced …

Kahan discretization is applicable to any system of ordinary differential equations on
$\mathbb R^ n $ with a quadratic vector field, $\dot {x}= f (x)= Q (x)+ Bx+ c $, and produces a …

On the singularity structure of Kahan discretizations of a class of quadratic vector fields |
European Journal of Mathematics Skip to main content SpringerLink Log in Menu Find a journal …

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 involution …

We discretise the Lax pair for the reduced Nahm systems and prove its equivalence with the
Kahan–Hirota–Kimura discretisation procedure. We show that these Lax pairs guarantee the …

We find a novel one-parameter family of integrable quadratic Cremona maps of the plane
preserving a pencil of curves of degree 6 and of genus 1. They turn out to serve as Kahan …

We show how to construct in an elementary way the invariant of the KHK discretisation of a
cubic Hamiltonian system in two dimensions. That is, we show that this invariant is …