Local controllability at critical points and generic systems in 3-space (Q1919596)

A triplet of \(C^k\), \(k \geq 3\), vector fields is considered on a three-dimensional smooth and connected manifold under generic assumptions. Necessary conditions and sufficient conditions for local controllability (but not for small-time local controllability) at a critical point of one of them are proved. The obtained results are used to determine the local controllability of affine control systems at nonrelative equilibrium points or with one-sided controls. Some illustrative examples are presented.