Geodesic
Families of vector fields which generate the group of diffeomorphisms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 147-160.

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Given a compact manifold $M$ and a family of vector fields $\mathcal F$ such that the group generated by $\mathcal F$ acts transitively on $M$, we prove that the group of all diffeomorphisms of $M$ that are isotopic to the identity is generated by the exponentials of vector fields in $\mathcal F$ rescaled by smooth functions. 
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     author = {Marco Caponigro},
     title = {Families of vector fields which generate the group of diffeomorphisms},
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Marco Caponigro. Families of vector fields which generate the group of diffeomorphisms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 147-160. http://geodesic.mathdoc.fr/item/TM_2010_270_a9/

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