Abstract

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 S-2 approximate to C boolean OR {infinity} by Mobius 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 [J. Differential Equations, 39 (1981), pp. 186-211].