Geodesic
Invariant measures and controllability of finite systems on compact manifolds
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 643-655

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A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956-973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

DOI : 10.1051/cocv/2011165
Classification : 17B66, 37A05, 37N35, 93B05, 93B17, 93C10
Keywords: compact homogeneous spaces, linear systems, controllability, finite dimensional Lie algebras, Haar measure 
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     title = {Invariant measures and controllability of finite systems on compact manifolds},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {643--655},
     publisher = {EDP-Sciences},
     volume = {18},
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     doi = {10.1051/cocv/2011165},
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     zbl = {1281.93020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011165/}
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Jouan, Philippe. Invariant measures and controllability of finite systems on compact manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 643-655. doi: 10.1051/cocv/2011165

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