KAM理论下的一类哈密顿系统双曲不变环面的保持性

On The Persistence for A Class of Hyperbolic Hamiltonian Systems by KAM Theory

利用哈密顿系统在辛坐标变换下的不变性,考虑一类近可积哈密顿系统:H(q,p,z)=h(p)+12〈Az,z〉+f(q,p,z),在不假设任何非退化条件下,证明了如果在某丢番频率处频率映射有非零拓扑度,则双曲不变环面在扰动下保持.

By the persistence of Hamiltonian system under symplectie transformation, we consider a class of nearly integrable Hamiltonian systems, H（q,p, z） =h （p） ＋ 1/2 （Az, z） ＋f （q, p, z）. Without assuming any non-degeneracy condition, we prove that if the frequency mapping has nonzero topological degree at some Diophantine frequency, then the hyperbolic invariant to- rus persist under small perturbations.