Controllability on sl(2, ℂ) with restricted controls

In this paper we study controllability of affine invariant control systems on the group Sl(2, C) with restricted controls. We develop a method based on the action of Sl(2, ℂ) on the sphere S² ≈ ℂ ∪ {∞} by Möbius functions. Some controllability results are proved. It is proved also that controllability with restricted controls is not a generic property, contrary to the case of unrestricted controls, as proved in the classic paper by Jurdjevic and Kupka.