The main result of this paper is the discretization of Hamiltonian systems of the form $\ddot
x=-K\nabla W (x) $, where $ K $ is a constant symmetric matrix and $ W\colon\mathbb {R} …

Kahan discretization is applicable to any quadratic vector field and produces a birational
map which approximates the shift along the phase flow. For a planar quadratic canonical …

In this paper we use the method of discrete Darboux polynomials to calculate preserved
measures and integrals of rational maps. The approach is based on the use of cofactors and …

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 …

Kahan discretization is applicable to any quadratic vector field and produces a birational
map which approximates the shift along the phase flow. For a planar quadratic Hamiltonian …

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 …

How one can repair non-integrable Kahan discretizations - IOPscience Skip to content IOP
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On the singularity structure of Kahan discretizations of a class of quadratic vector fields |
European Journal of Mathematics Skip to main content Springer Nature Link Account Menu …

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 …