Dynamical systems on manifolds: Accessibility and controllability

A brief survey of recent results on nonlinear controllability is presented, and a new theorem is stated and proved, giving an "exact time" analogue of Chow\´s Theorem. In a series of recent papers (Brockett[1], Haynes and Hermes[4], Ku??era[7][8], Lobry[9][10], Jurdjevic and Sussmann[5], Sussmann[12][13][14], Sussmann and Jurdjevic[15]) the methods of Differential Geometry have been applied to the study of accessibility and controllability problems for non-linear systems. We shall survey some aspects of this recent work.