Families of vector fields which generate the group of diffeomorphisms

TL;DR

This paper proves that certain families of vector fields on a compact manifold, which are bracket generating and invariant under multiplication, generate the entire connected component of the identity in the diffeomorphism group.

Contribution

It establishes a new criterion for families of vector fields to generate the identity component of the diffeomorphism group on compact manifolds.

Findings

Bracket generating families generate the connected component of the identity in Diff(M)

Invariant families under multiplication suffice for generation

Results apply to smooth functions on compact manifolds

Abstract

Given a compact manifold M, we prove that any bracket generating and invariant under multiplication on smooth functions family of vector fields on M generates the connected component of unit of the group Diff(M).