一类拟周期哈密顿系统在弱非退化条件下的约化性

The reducibility of a class of quasi-periodic Hamiltonian systems under weaker nondegeneracy conditions

考虑平衡点附近一类拟周期非线性哈密顿系统在弱非退化条件下的约化性问题.证明在弱非退化条件和非共振条件下,对于绝大多数充分小的参数ε,通过一个拟周期辛变换,非线性哈密顿系统是能约化的.

In this paper,we considered the reducibility of a class of quasi-periodic nonlinear Hamiltonian near the equilibrium.Under weaker non-degeneracy conditions and non-resonance conditions,by a quasi-periodic symplectic transformation,we proved that for most sufficiently smallε,the nonlinear Hamiltonian system could be reducible.