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Proceedings of the American Mathematical Society

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On the completeness of Hamiltonian vector fields

Author: William B. Gordon
Journal: Proc. Amer. Math. Soc. 26 (1970), 329-331
MSC: Primary 34.65; Secondary 53.00
MathSciNet review: 0276574
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Abstract: Sufficient conditions are given for a hamiltonian vector field to be complete which involve bounds on the potential or its gradient.

References [Enhancements On Off] (What's this?)

  • [1] R. Abraham, Foundations of mechanics, Benjamin, New York, 1967. MR 36 #3527.
  • [2] Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
  • [3] John Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. (2) 63 (1956), 20–63. MR 0075639

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Keywords: Complete vector field, hamiltonian vector field
Article copyright: © Copyright 1970 American Mathematical Society