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Completeness of Hamiltonian vector fields


Author: David G. Ebin
Journal: Proc. Amer. Math. Soc. 26 (1970), 632-634
MSC: Primary 57.55; Secondary 34.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0278340-X
MathSciNet review: 0278340
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Abstract: We prove that under certain conditions the flow of a Hamiltonian vector field on a possibly infinite-dimensional dynamical system exists for all time.


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

  • [1] R. Abraham, Foundations of mechanics, Benjamin, New York, 1967. MR 36 #3527.
  • [2] P. Dombrowski, On the geometry of the tangent bundle, J. Reine Angew. Math. 210 (1962), 73-88. MR 25 #4463. MR 0141050 (25:4463)
  • [3] W. Gordon, On completeness of vector fields (preprint). MR 1794196
  • [4] S. Lang, Introduction to differentiable manifolds, Interscience, New York, 1962. MR 27 #5192. MR 0155257 (27:5192)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0278340-X
Keywords: Hamiltonian vector field, Hilbert manifold, Riemannian structure, symplectic two-form, vertical subspace, horizontal subspace, spray, complete metric
Article copyright: © Copyright 1970 American Mathematical Society

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