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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
DOI: https://doi.org/10.1090/S0002-9939-1979-0534415-7
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] N. I. Akhiezer, The calculus of variations (Transl., Aline H. Frink), Ginn/Blaisdell, Waltham, Mass., 1962. MR 0142019 (25:5414)
  • [2] F. H. Clarke, Periodic solutions to Hamiltonian inclusions (to appear). MR 614215 (83a:58035)
  • [3] P. H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 157-184. MR 0467823 (57:7674)
  • [4] A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math. 20 (1973), 47-57. MR 0328222 (48:6564)
  • [5] -, Periodic orbits for convex Hamiltonian systems, Ann. of Math. (to appear).

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Additional Information

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

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