Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to
describe the recent progress in nonlinear differential equations and nonlinear dynamical …

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

We propose a geometric construction of three-dimensional birational maps that preserve two
pencils of quadrics. The maps act as compositions of involutions, which, in turn, act along …

We present linearly implicit methods that preserve discrete approximations to local and
global energy conservation laws for multisymplectic partial differential equations with cubic …

A novel integration method for quadratic vector fields was introduced by Kahan in 1993.
Subsequently, it was shown that Kahan's method preserves a (modified) measure and …

The numerical method of Kahan applied to quadratic differential equations is known to often
generate integrable maps in low dimensions and can in more general situations exhibit …

Aromatic B-series were introduced as an extension of standard Butcher-series for the study
of volume-preserving integrators. It was proven with their help that the only volume …

In this letter we propose a systematic approach for detecting and calculating integrals and
preserved measures of rational maps. The approach is based on the use of cofactors and …

Given a quadratic vector field on possessing a quadratic first integral depending on two of
the independent variables, we give a constructive proof that Kahan's discretization method …

Motivated by the study of the Kahan–Hirota–Kimura discretisation of the Euler top, we
characterise the growth and integrability properties of a collection of elements in the …