ИСТИНА

We analyze controllability of generic dynamic inequalities with locally bounded derivatives on two dimensional sphere (or two-dimensional smooth manifold) and show that it local controllability properties are stable. We prove that the structural stability of such inequalities on a sphere is equivalent to their structural stability on a plane either in the case of complete controllability or the absence of admissible velocities near infinity. In particular, the typical simplest inequality on a sphere is structurally stable