J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respecti...J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi＇s definition. In the end of the paper, we calculate the Mane set and Aubry set for a single pendulum system.展开更多
The Chinese masters of the seventeenth century inspire luxury brand Chanel Some brands like Chanel continually put on the market products that carry an element of dream: an
文摘J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi＇s definition. In the end of the paper, we calculate the Mane set and Aubry set for a single pendulum system.
文摘The Chinese masters of the seventeenth century inspire luxury brand Chanel Some brands like Chanel continually put on the market products that carry an element of dream: an
