# Invariant measures and controllability of finite systems on compact manifolds

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 3, page 643-655
- ISSN: 1292-8119

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topJouan, Philippe. "Invariant measures and controllability of finite systems on compact manifolds." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 643-655. <http://eudml.org/doc/277822>.

@article{Jouan2012,

abstract = {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. },

author = {Jouan, Philippe},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Compact homogeneous spaces; linear systems; controllability; finite dimensional Lie algebras; Haar measure; compact homogeneous spaces},

language = {eng},

month = {11},

number = {3},

pages = {643-655},

publisher = {EDP Sciences},

title = {Invariant measures and controllability of finite systems on compact manifolds},

url = {http://eudml.org/doc/277822},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Jouan, Philippe

TI - Invariant measures and controllability of finite systems on compact manifolds

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/11//

PB - EDP Sciences

VL - 18

IS - 3

SP - 643

EP - 655

AB - 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.

LA - eng

KW - Compact homogeneous spaces; linear systems; controllability; finite dimensional Lie algebras; Haar measure; compact homogeneous spaces

UR - http://eudml.org/doc/277822

ER -

## References

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