On autonomous control systems on certain manifolds

Liang, Chao Chu

doi:10.1090/S0002-9939-1980-0560585-9

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On autonomous control systems on certain manifolds
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by Chao Chu Liang

Proc. Amer. Math. Soc. 79 (1980), 63-66

DOI: https://doi.org/10.1090/S0002-9939-1980-0560585-9

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Abstract:

Let ${M^n}$ be a compact ${C^\infty }$ manifold, $n \geqslant 4$, admitting a vector field with every orbit a circle. Then there exists a completely controllable set S consisting of two nonsingular ${C^\infty }$ vectors X and Y such that every orbit of X is a circle.

References

Daniel Asimov, Round handles and non-singular Morse-Smale flows, Ann. of Math. (2) 102 (1975), no. 1, 41–54. MR 380883, DOI 10.2307/1970972
Norman Levitt and Héctor J. Sussmann, On controllability by means of two vector fields, SIAM J. Control 13 (1975), no. 6, 1271–1281. MR 0402812