|
In this article, we develop a parametrized weak KAM technique, whichcan be regarded as a generalization from the finite dimensional case to the infinite dimensional case of partial results in the weak KAM theory. In such a framework, applying the technique to the nearly integrable convex Hamiltonian systems locally, we obtain the existence of lower dimensional action minimizing measures. The lower dimensional invariant sets, which support the action minimizing measures, are generalizations of lower dimensional invariant tori. Furthermore, we attempt to generalize our main result to the nonconvex case. Under certain weaker conditions than strict convexity, we still provide an existence result of lower dimensional action minimizing measures for the nearly integrable Hamiltonian systems. |
|
Keywords:Hamiltonian systems; lower dimensional action minimizing measures; nearly integrable Hamiltonian systems; weak KAM theory |
|