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]

Survey:

• S. Blanes, F. Casas, J. A. Oteo, J. Ros, The Magnus expansion and some of its application, Physics reports 470 (2008) 151–238 doi

See also:

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