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Controllability on the Group of Diffeomorphisms A. A. Agracheva,b

Summary: Controllability on the Group of Diffeomorphisms
A. A. Agracheva,b
, M. Caponigro,b,1
aSteklov Mathematical Institute, Gubkina str. 8, 119991, Moscow, Russia
bSISSA, Via Beirut 2-4, 34014, Trieste, Italy
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 diffeomor-
phisms of M.
Soit M une vari´et´e compacte, nous montrons que toute famille de champs de
vecteurs satisfaisant la condition du rang et ´etant invariante par multiplication
par fonctions lisses engendre la composante connexe de l'identit´e du groupe
Key words: Controllability, Diffeomorphisms, Geometric Control
2000 MSC: 93B05, 58D05
1. Introduction
In this paper we give a simple sufficient condition for a family of flows on a
compact smooth manifold M to generate the group Diff0(M) of all diffeomor-


Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)


Collections: Engineering; Mathematics