A remark on nonlinear accessibility conditions and infinite prolongations

The Lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order. It yields to a new Lie algebraic criterion and to the consideration of first integrals, which apply to nonlinear systems in quite general form; the latter characterization in particular is valid without distinguishing between the system variables and is independent of time-scalings. Weak accessibility is also considered.