On discretization of the Euler top

TL;DR

This paper explores the use of intersection theory to develop new finite-difference discretizations of the Euler top that preserve integrals of motion and Poisson structure, enhancing numerical integrability.

Contribution

It introduces novel discretizations of the Euler top that maintain key integrable properties, advancing numerical methods for classical integrable systems.

Findings

Discretizations preserve integrals of motion

Discretizations maintain Poisson structure up to scaling

New methods improve numerical stability for Euler top

Abstract

Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing the integrals of motion with the continuous time system and the Poisson bracket up to the integer scaling factor.