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| In this article, we study the existence of action minimizing measures for a class of nearly integrable, generalized Hamiltonian systems. The invariant sets, which support the action minimizing measures, are generalizations of invariant tori.The proof in this paper is variational in nature, and involves the minimization of the functional introducedby Evans L.. After giving an a priori estimate of gradients of the minimizers and defining thegeneralized Legendre transformation, a modified version of weak KAM techniques is available to obtain action minimizing measures for the generalized Hamiltonian system. |
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| Keywords:generalized Hamiltonian systems; action minimizing measures; weak KAM theory |
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