The Magnus expansion and Post-Lie algebras

TL;DR

This paper explores the relationship between the classical Magnus expansion and Post-Lie algebras, connecting algebraic and geometric perspectives to enhance understanding of Lie group integrators.

Contribution

It introduces a novel connection between the Magnus expansion and Post-Lie algebras, providing a unified framework for Lie group integrators.

Findings

Relates classical and post-Lie Magnus expansions

Places Magnus expansion within Lie group integrator context

Uses algebraic and geometric arguments to unify concepts

Abstract

We relate the classical and post-Lie Magnus expansions. Intertwining algebraic and geometric arguments allows to placing the classical Magnus expansion in the context of Lie group integrators.