Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C35, 49H05, 58F05

Retrieve articles in all journals with MSC: 34C35, 49H05, 58F05

Additional Information

Keywords: Hamilton's equations, periodic orbit, Legendre transform
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society