Tracking a full Superconducting Super Collider (SSC) lattice to determine the long‐term dynamic aperture is very computer‐intensive. The author argues that low‐order maps (≤9) may have enough information to determine long‐term apertures. However, evaluating such maps is not trivial and can consume more time than tracking the original lattice. The author describes a way to construct an ‘‘equivalent’’ one‐turn map consisting of a small number of kicks, which to any specific order has the same generator as the original map, and minimizes spurious high‐order terms. For a ninth‐order map, the number of kicks is 36, and can be evaluated 50 times faster than SSC element‐by‐element tracking. Perhaps more importantly, the conjecture that low‐order terms of the map determine long‐term behavior can be tested. An affirmative result would allow simulation of the SSC in the Tevatron by adding a suitable set of nonlinear lenses. © 1995American Institute of Physics