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 …

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 …

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 …

We revisit the Kahan–Hirota–Kimura discretization of a quadratic vector field. The
corresponding discrete system is generated by successive iterations of a birational map F h …

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 …

In the context of integrable difference equations on quad-graphs, we introduce the method of
open boundary reductions, as an alternative to the well-known periodic reductions, for …

A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves
Page 1 Symmetry, Integrability and Geometry: Methods and Applications SIGMA 17 (2021) …

In dieser Arbeit behandeln wir verschiedene Aspekte zur Integrabilität von birationalen
Abbildungen, vorrangig im Kontext von Abbildungen, welche als Kahan-Diskretisierung von …