×

zbMATH — the first resource for mathematics

Orbits of families of vector fields and integrability of distributions. (English) Zbl 0274.58002

MSC:
58A30 Vector distributions (subbundles of the tangent bundles)
37-XX Dynamical systems and ergodic theory
34H05 Control problems involving ordinary differential equations
34C40 Ordinary differential equations and systems on manifolds
93B05 Controllability
93B03 Attainable sets, reachability
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Claude Chevalley, Theory of Lie groups. I, Princeton University Press, Princeton, N. J., 1946 1957. · Zbl 0063.00842
[2] Wei-Liang Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann. 117 (1939), 98 – 105 (German). · Zbl 0022.02304 · doi:10.1007/BF01450011 · doi.org
[3] SigurÄ’ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.
[4] Robert Hermann, On the accessibility problem in control theory, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 325 – 332.
[5] Claude Lobry, Contrôlabilité des systèmes non linéaires, SIAM J. Control 8 (1970), 573 – 605 (French). · Zbl 0207.15201
[6] Michihiko Matsuda, An integration theorem for completely integrable systems with singularities, Osaka J. Math. 5 (1968), 279 – 283. · Zbl 0169.24202
[7] Tadashi Nagano, Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan 18 (1966), 398 – 404. · Zbl 0147.23502 · doi:10.2969/jmsj/01840398 · doi.org
[8] Héctor J. Sussmann and Velimir Jurdjevic, Controllability of nonlinear systems, J. Differential Equations 12 (1972), 95 – 116. · Zbl 0242.49040 · doi:10.1016/0022-0396(72)90007-1 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.