Invariant tori and subharmonic bifurcations from periodic manifolds

The Floquet method is refined to establish a suitable local coordinate syst em along a periodic orbit situated in a periodic manifold. Then the averagi ng method and the theories of integral manifolds and the Fenichel's invaria nt manifolds are used to show the existence and the normal hyperbolicity of invariant tori and subhomoclinic orbits. Most traditional hypotheses are d iscarded, and most known results are extended. An example is given.