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Commutators of flows and fields

Markus Mauhart·Peter W. Michor
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Abstract

The well known formula $[X,Y]=\tfrac12\tfrac{\partial^2}{\partial t^2}|_0 (\Fl^Y_{-t}ø\Fl^X_{-t}ø\Fl^Y_tø\Fl^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.

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Markus Mauhart, Peter W. Michor. 1992-04-01. Commutators of flows and fields. https://arxiv.org/abs/math/9204221

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