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Periodic Solutions of Hamilton's Equations and Local Minima of the Dual Action
Frank H. Clarke
Transactions of the American Mathematical Society
Vol. 287, No. 1 (Jan., 1985), pp. 239-251
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2000408
Page Count: 13
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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.
Transactions of the American Mathematical Society © 1985 American Mathematical Society