  We show how solutions of a non--linear differential equation can be written
as sum indexed by planar trees: the Butcher series. Then we use that property
in order to control non--linear differential equation. We show that if the
linearized system is controllable then the system itself is controllable if the
nonlinear term is small enough and we express explicitly the control as a sum
indexed by planar tree which each terms is obtained by minimization of a
functional.
