We study groups and semigroups whish are generated by analytic families of diffeomorphisms. The central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold, which generalizes the familiar notion of local controllability of control systems with continuous, as well as discrete time. Lie theory methods are used. We systematically explot the so called fast switching variations and properties of the jet spaces of curves on the state manifold.
Title: Local controllability for families of diffeomorphisms
Authors: A.A. Agrachev, R.V. Gamkrelidze
Journal title: Systems and Control Letters