## Transitivity of families of invariant vector fields on the semidirect products of Lie groups.(English)Zbl 0519.49023

### MSC:

 93B03 Attainable sets, reachability 53A04 Curves in Euclidean and related spaces 93B05 Controllability 17B99 Lie algebras and Lie superalgebras 22E60 Lie algebras of Lie groups 57R25 Vector fields, frame fields in differential topology 57R27 Controllability of vector fields on $$C^\infty$$ and real-analytic manifolds

Zbl 0237.93027
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### References:

 [1] V. Jurdjevic, On the reachability properties of curves in $${{\mathbf{R}}^n}$$ with prescribed curvatures, University of Bordeaux Publ. 1, no. 8009, 1980. [2] V. Jurdjevic and I. Kupka, Control systems subordinated to a group action: accessibility, J. Differential Equations 39 (1981), no. 2, 186 – 211. · Zbl 0531.93008 [3] Velimir Jurdjevic and Héctor J. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972), 313 – 329. · Zbl 0237.93027 [4] Arthur J. Krener, A generalization of Chow’s theorem and the bang-bang theorem to non-linear control problems, SIAM J. Control 12 (1974), 43 – 52. · Zbl 0243.93008 [5] C. Lobry, Controllability of non-linear systems on compact manifolds, SIAM J. Control Optim. 1 (1974), 1-4. · Zbl 0286.93006 [6] Héctor J. Sussmann and Velimir Jurdjevic, Controllability of nonlinear systems, J. Differential Equations 12 (1972), 95 – 116. · Zbl 0242.49040
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