正定哈密尔顿系统的局部极小轨道和弱KAM解

本项目就正定Hamilton系统的局部极小轨道和弱KAM解的若干问题展开研究。一是在解析扰动下或仅势能扰动下弱KAM解的摄动问题，以期得到预双曲正定Hamilton系统连接轨道的解析通有性等；二是局部极小轨道与相关生成函数的问题，以期就正定哈密尔顿系统建立基于局部极小轨道而构造大范围全局连接轨道的方法，从而有可能构造在相空间任意游走的连接轨道。

In this project, we are going to study some problems about locally minimal curves and weak-KAM solutions exhibited by positive definite Hamilton systems. The first one is about the perturbation of weak-KAM solutions when the Hamilton system is under analytical perturbation or potential perturbation. Another one is to study locally minimal orbits for each cohomoloy class and to investigate whether there exists relevant generating function, so that to establish certain method to construct global connecting orbits, which allows one to construct orbits possibly dense in phase space.