Geodesic
Commutators of flows and fields
Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 229-236.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The well known formula $[X,Y]=\tfrac{1}{2}\tfrac{\partial ^2}{\partial t^2}|_0 (^Y_{-t}ø^X_{-t}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
Classification : 37C10, 58F25
Keywords: commutators; flows; vector fields 
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     title = {Commutators of flows and fields},
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Mauhart, Markus; Michor, Peter W. Commutators of flows and fields. Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 229-236. http://geodesic.mathdoc.fr/item/ARM_1992__28_3-4_a11/