周期流形的不变环面和次调和分支

Invariant Tori and Subharmonic BIfurcations from Periodic Manifolds

本文通过精华Ｆｌｏｑｕｅｔ方法在周期流形的周期轨道邻域建立起适当的局部坐标，然后应用平均法和积分流形及Ｆｅｎｉｃｈｅｌ不变流形理论来证明不变环面和次调和轨道的存在性和法向双曲性．大多数传统的假设被放弃，而大多数已知的结果被推广．

The Floquet method is refined to establish a suitable local coordinates along a periodic orbit situated in a periodic manifold. Then the averaging and the theories of integral manifolds and the Fenichel′s invariant manifolds are used to show the existence and the normal hyperbolicity of invariant tori and subhomoclinic orbits.Most traditional hypotheses are discarded, and most known results are extended. An example is given.