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On autonomous control systems on certain manifolds


Author: Chao Chu Liang
Journal: Proc. Amer. Math. Soc. 79 (1980), 63-66
MSC: Primary 49E15; Secondary 57R27
DOI: https://doi.org/10.1090/S0002-9939-1980-0560585-9
MathSciNet review: 560585
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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 [Enhancements On Off] (What's this?)

  • [1] D. Asimov, Round handles and non-singular Morse-Smale flows, Ann. of Math. (2) 102 (1975), 41-54. MR 0380883 (52:1780)
  • [2] N. Levitt and H. J. Sussmann, On controllability by means of two vector fields, SIAM J. Conrol 13 (1975), 1271-1281. MR 0402812 (53:6626)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560585-9
Keywords: Completely controllable set of vector fields, orbits, trajectory, round handle decomposition of a manifold
Article copyright: © Copyright 1980 American Mathematical Society

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