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Chronological algebras and nonstationary vector fields. (English. Russian original) Zbl 0473.58021

J. Sov. Math. 17, 1650-1675 (1981); translation from Itogi Nauki Tekh., Ser. Probl. Geom. 11, 135-176 (1980).

MSC:

37C10 Dynamics induced by flows and semiflows
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
49Q99 Manifolds and measure-geometric topics
34C40 Ordinary differential equations and systems on manifolds
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References:

[1] A. A. Agrachev, ?A necessary condition for optimality of the second order in the general nonlinear case,? Mat. Sb.,102, No. 4, 551?568 (1977).
[2] A. A. Agrachev and R. V. Gamkrelidze, ?A second order optimality principle for high speed problems,? Mat. Sb.,100, No. 4, 610?643 (1976).
[3] A. A. Agrachev and R. V. Gamkrelidze, ?Exponential representation of flows and the chronological calculus,? Mat. Sb.,107, No. 4, 467?532 (1978). · Zbl 0408.34044
[4] R. Gabasov and F. M. Kirillova, Singular Optimal Equations [in Russian], Nauka, Moscow (1973). · Zbl 0211.18401
[5] J.-P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin (1965).
[6] R. Gamkrelidze, ?Exponential representation of solutions of ordinary differential equations,? Proc. Equadiff. Fifth Conference Prague 1977, Springer-Verlag (1978).
[7] H. Hermes, ?Local controllability and sufficient conditions in singular problems. I; II,? J. Diff. Eq.,20, No. 1, 213?232 (1976); SIAM J. Control.,14, No. 6, 1049?1062 (1976). · Zbl 0282.93010
[8] H. J. Kelly, R. E. Kopp, and H. G. Moyer, Singulary Extremals. Topics in Optimization, Academic Press (1967).
[9] H. W. Knobloch, ?High order necessary conditions and local controllability,? Math. Inst. der Univ. Würzburg (1978) (preprint).
[10] A. J. Krener, ?The high order maximal principle and its applications to singular extremals,? SIAM J. Control,15, No. 2, 256?293 (1977). · Zbl 0354.49008
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