E1ementary Bifurcations of Non—Critical but N0n—Hyperbolic Invariant Tori

Consider the time-periodic peturbations of n-dimensional autonomous systems with non-hyperbolic but non-critical closed orbits in the phase space.The elementary bifurcations,such as the saddle-node,transcritical,pitchfork bifurcation to a non-hyperbolic but non-critical invariant torus of the unperturbed systems in the extended phase space(x,t),are sutdied.Some conditions which depend only on ithe original systems and can be used to determine the bifurcation structures of these problems are obtained.The theory is applied to two concrete examples.