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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Periodic solutions of Hamilton's equations and local minima of the dual action


Author: Frank H. Clarke
Journal: Trans. Amer. Math. Soc. 287 (1985), 239-251
MSC: Primary 58F05; Secondary 34C25, 58E30, 58F22, 70H05
MathSciNet review: 766217
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Abstract: The dual action is a functional whose extremals lead to solutions of Hamilton's equations. Up to now, extremals of the dual action have been obtained either through its global minimization or through application of critical point theory. A new methodology is introduced in which local minima of the dual action are found to exist. Applications are then made to the existence of Hamiltonian trajectories having prescribed period.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0766217-8
PII: S 0002-9947(1985)0766217-8
Keywords: Periodic trajectories, dual action, convex Hamiltonians
Article copyright: © Copyright 1985 American Mathematical Society