Abstract
This article gives a very simple algorithm which allows to immediately write down a canonical nonlinear representation of a free nilpotent Lie algebra. Specifically, it defines a set of local coordinates and gives a formula for the components of a set of system vector fields in terms of these coordinates. The components of iterated Lie brackets of the system vector fields can also be read off easily without any further differentiation. The formulae given here are very close to Sussmann’s product expansion of the Chen-Fliess series and to the chronological calculus introduced by Agrachev and Gamkrelidze.
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