【摘要】 本文给出了关于哈密顿系统低维环面的一个推广的KAM定理,它适用于同时存在法向频率和双曲法向分量的情况.其证明基于尤建功的一个定理的光滑性表述及法向双曲不变流形理论的应用.文中还给出了另外两种情况下的推广.更多还原

【Abstract】 A generalized KAM theorem for lower dimensional tori in Hamiltonian systems is obtained, which applies to the case where there are normal frequencies and hyperbolic normal components simultaneously. The proof is based on the combination of a smoothness of J. G. You’s theorem and the theory of normally hyperbolic invariant manifolds. Two other generalizations are also given.更多还原