Poisson integrators for Lie–Poisson structures on

Abstract

This paper is concerned with the study of Poisson integrators. We are interested in Lie–Poisson systems on . First, we focus on Poisson integrators for constant Poisson systems and the transformations used for transforming Lie–Poisson structures to constant Poisson structures. Then, we construct local Poisson integrators for Lie–Poisson systems on . Finally, we present the results of numerical experiments for two Lie–Poisson systems and compare our Poisson integrators with other known methods.