Stability domain of planar symplectic maps using invariant manifolds

In a previous paper we showed that, for the one-parameter areapreserving H enon map, the domain in phase space where stable motion occurs can always be computed by using the invariant manifolds emanating from the hyperbolic xed point of period one, regardless of the value of the parameter. We present here a generalization of this result to a large class of symplectic polynomial mappings of the plane. Even in this case it is possible to show that the stability domain is given by the inner envelope of the invariant manifolds of a low period (one or two) hyperbolic xed point. Numerical simulations are presented. They were performed on di erent maps, including a model of relevance for accelerator physics.