What is the Magnus Expansion?
arXiv:2312.16674 · doi:10.3934/jcd.2024028
Abstract
The Magnus expansion, introduced by Wilhelm Magnus in 1954, is an infinite Lie series employed to express solutions for first-order homogeneous linear differential equations involving a linear operator. Since its discovery it has evolved into a pivotal tool used across diverse disciplines, including physics, chemistry, and engineering. Over the past 25 years, the Magnus expansion has undergone significant mathematical developments which revealed an intricate interplay between algebra, combinatorics, and geometry. By emphasizing a modern perspectives based on the use of pre- and post-Lie algebras, we discuss the Magnus expansion from the viewpoint of the notion of crossed morphism.
33 pages, final version
References in corpus (11)
- The Magnus expansion and some of its applications
- Homology of generalized partition posets
- On post-Lie algebras, Lie--Butcher series and moving frames
- Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation
- Post-Lie algebras and factorization theorems
- The Magnus expansion and Post-Lie algebras
- On expansions for nonlinear systems, error estimates and convergence issues
- The pre-Lie structure of the time-ordered exponential
- Post-symmetric braces and integration of post-Lie algebras
- Algebraic aspects of connections: from torsion, curvature, and post-Lie algebras to Gavrilov's double exponential and special polynomials
- From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras