Computation of the Dynamic Aperture of 2D Generic Maps Using Invariant Manifolds

In this paper the phase-space of generic 2D area-preserving polynomial mappings is studied. These mappings modelize the transverse dynamics of a flat beam in a circular machine dominated by non-linear magnetic errors. In particular, the problem of computing the dynamic aperture, i.e., the region in phase-space where stable motion occurs, is considered. The main result is that the boundary of the stability domain is given by the invariant manifolds emanating from the outermost unstable fixed point of low period (one or two). This study extends previous results obtained for reversible area-preserving polynomial maps of the plane.