Application of Variational Method in Hamiltonian Dynamical Systems
Lagrangian variational method boosts the qualitative research of Hamiltonian dynamical systems greatly.The motivation of this method is to make partitions of the invariant sets by the"variational minimum",and parametrize them into a foliation with respect to the homology(cohomology)group.Making use of the fine properties of such a structure,the global dynamics and the generic features of invariant sets can be revealed.In these years this method has been applied to other subjects,e.g.the partial differential equations,optimal controls,etc.In some practical occasions,it also makes great effects.This paper analyses the front problems of this subject with details.It exhibits the achievements of Chinese experts and the associated advantages.Besides,it concisely summarizes the development of the variational method in Hamiltonian systems,and the useful experiences within it,and finally programs the new trend of this subject clearly.
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