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A classical variational principle for periodic Hamiltonian trajectories


Author: Frank H. Clarke
Journal: Proc. Amer. Math. Soc. 76 (1979), 186-188
MSC: Primary 34C35; Secondary 49H05, 58F05
MathSciNet review: 534415
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Abstract: Using only classical theorems of the calculus of variations, the existence of periodic solutions to Hamilton's equations on a given convex energy surface is proved.


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

  • [1] Naum I. Akhiezer, The calculus of variations, Translated from the Russian by Aline H. Frink. A Blaisdell Book in the pure and Applied Sciences, Blaisdell Publishing Co. (A Division of Random House, Inc.), New York-London, 1962. MR 0142019
  • [2] Frank H. Clarke, Periodic solutions to Hamiltonian inclusions, J. Differential Equations 40 (1981), no. 1, 1–6. MR 614215, 10.1016/0022-0396(81)90007-3
  • [3] Paul H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), no. 2, 157–184. MR 0467823
  • [4] Alan Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math. 20 (1973), 47–57. MR 0328222
  • [5] -, Periodic orbits for convex Hamiltonian systems, Ann. of Math. (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0534415-7
Keywords: Hamilton's equations, periodic orbit, Legendre transform
Article copyright: © Copyright 1979 American Mathematical Society