Equicontinuous system

Summary

An equicontinuous system is a topological dynamical system whose family of iterates $\set{f^n : n \ge 0}$ is equicontinuous. Then points that start close stay close for all future times, uniformly in time. Isometries are the typical examples, such as rotations of the circle or translations on a compact group. Equicontinuity is the opposite of sensitive dependence on initial conditions, so equicontinuous systems are the most orderly ones in topological dynamics.