Local controllability along a reference trajectories (Q1176160)

Local controllability along a reference trajectory of analytic and smooth affine single input control systems (without any a priori bounds on the control) is considered. The main purpose of the paper is to give a geometric proof of a version of the Hermes conjecture for local controllability along a reference trajectory previously proved for local controllability at a point and generalizing to arbitrary dimensions the result by \textit{H. Hermes} [SIAM J. Control Optimization 20, 211-220 (1982; Zbl 0486.49022)].