id: 06339545
dt: j
an: 06339545
au: Ebrahimi-Fard, Kurusch; Manchon, Dominique
ti: The Magnus expansion, trees and Knuth’s rotation correspondence.
so: Found. Comput. Math. 14, No. 1, 1-25 (2014).
py: 2014
pu: Springer US, New York, NY
la: EN
cc:
ut: Magnus expansion; B-series; trees; pre-Lie algebra; dendriform algebra;
Rota-Baxter algebra; permutations
ci:
li: doi:10.1007/s10208-013-9172-x
ab: Summary: W.~Magnus introduced a particular differential equation
characterizing the logarithm of the solution of linear initial value
problems for linear operators. The recursive solution of this
differential equation leads to a peculiar Lie series, which is known as
Magnus expansion, and involves Bernoulli numbers, iterated Lie brackets
and integrals. This paper aims at obtaining further insights into the
fine structure of the Magnus expansion. By using basic combinatorics on
planar rooted trees we prove a closed formula for the Magnus expansion
in the context of free dendriform algebra. From this, by using a
well-known dendriform algebra structure on the vector space generated
by the disjoint union of the symmetric groups, we derive the
Mielnik-Plebański-Strichartz formula for the continuous
Baker-Campbell-Hausdorff series.
rv: