Geometric and integrability properties of Kahan's method

Elena Celledoni, David McLaren, Brynjulf Owren, Reinout Quispel

Published 2018-05-22Version 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 discretization method exactly preserves a nearby modifed integral. Building on this result, we present a family of integrable quadratic vector fields (including the Euler top) whose Kahan discretization is a novel 10-parameter family of integrable maps.