# A.A. Agrachev, M. Caponigro, Controllability on the group of diffeomorphisms

Title: Controllability on the group of diffeomorphisms
Authors: A.A. Agrachev, M. Caponigro
Journal title: Annales de l'Institut Henri Poincare`- Analyse non lineaire
Year: 2009
Volume: 26
Pages: 2503-2509
Abstract:

Given a compact manifold $M$, we prove that any bracket generating family of vector fields on $M$, which is invariant under multiplication by smooth functions, generates the connected component of the identity of the group of diffeomorphisms of $M$.