Integral representation for bracket-generating multi-flows

Ermal Feleqi, Franco Rampazzo

If $f_1,f_2$ are smooth vector fields on an open subset of an Euclidean space and $[f_1,f_2]$ is their Lie bracket, the asymptotic formula $$Ψ_{[f_1,f_2]}(t_1,t_2)(x) - x =t_1t_2 […