For the Superconducting Super Collider (SSC) dynamic aperture study, one‐turn‐map tracking can be made nearly as reliable as element‐by‐element trackings. If a‐one‐turn map is sympletic and accurate to five or more digits in one‐turn tracking for the phase‐space coordinates of particles within the interest region (inside or around the dynamic aperature), then the one‐turn map is nearly as reliable as its associated element‐by‐element tracking for predicting the ‘‘global’’ long‐term stability of the storage ring.