Suspension flow

Summary

The suspension flow of an invertible map turns a discrete-time system into a continuous-time flow. Each point moves up at unit speed along a vertical segment whose height is given by a positive roof function. At the top it jumps to the base above the image point. The original map is recovered as the first-return map of the flow to the base. Suspensions with constant roof $1$ give the natural flow on the mapping torus. Suspensions with general roofs are a standard way to build examples of flows and to reduce flows to maps.