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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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R. Abraham, Foundations of mechanics, Benjamin, New York, 1967. MR 36 #3527.
- Peter Dombrowski, On the geometry of the tangent bundle, J. Reine Angew. Math. 210 (1962), 73–88. MR 141050, DOI https://doi.org/10.1515/crll.1962.210.73
- N. L. Belaya and N. N. Petrov, Completeness of vector fields, Vestnik St. Petersburg Univ. Math. 26 (1993), no. 4, 3–4. MR 1794196
- Serge Lang, Introduction to differentiable manifolds, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155257
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Additional Information
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