STABILITY DOMAIN OF PLANAR SYMPLECTIC MAPS USING INVARIANT-MANIFOLDS

In a previous paper [Phys. Lett. A 182, 255 (1993)] we showed that, fo r the one-parameter area-preserving Henon map, the domain in phase spa ce where stable motion occurs can always be computed by using the inva riant manifolds emanating from the hyperbolic fixed point of period on e, regardless of the value of the parameter. We present here a general ization of this result to a large class of symplectic polynomial mappi ngs of the plane. Even in this case it is possible to show that the st ability domain is given by the inner envelope of the invariant manifol ds of a low period (one or two) hyperbolic fixed point. Numerical simu lations are presented. They were performed on different maps, includin g a model of relevance for accelerator physics.