nLab Magnus expansion

Idea

The Magnus expansion is a continuous analogue of the Hausdorff series in Lie theory. It is the basis for some methods applying Lie theory to non-autonomous linear differential equations for linear operators.

Literature

The Magnus expansion was proposed in

• Wilhelm Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7 4 (1954) 649–673

  (1954) [doi:10.1002/cpa.3160070404]

Surveys:

• S. Blanes, F. Casas, J. A. Oteo, J. Ros, The Magnus expansion and some of its application, Physics reports 470 (2008) 151–238 doi
• Kurusch Ebrahimi-Fard, Igor Mencattini, Alexandre Quesney, What is the Magnus Expansion?, arXiv:2312.16674

Path signature generalized to surface signature (for surface iterated integrals) and related to Lie algebra crossed modules in

• Ilya Chevyrev, Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia, A multiplicative surface signature through its Magnus expansion, arXiv:2406.16856

A post-Lie algebra version

• M. J. H. Al-Kaabi, K. Ebrahimi-Fard, D. Manchon, Post-Lie Magnus expansion and BCH-recursion, SIGMA 18, (2022), 023, 16 pages.