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  "body": "\n## Summary\n\nAn equicontinuous system is a topological dynamical system whose family of iterates $\\set{f^n : n \\ge 0}$ is [[equicontinuous|0XN66MZN0Y]].\nThen points that start close stay close for all future times, uniformly in time.\nIsometries are the typical examples, such as rotations of the circle or translations on a compact group.\nEquicontinuity is the opposite of sensitive dependence on initial conditions, so equicontinuous systems are the most orderly ones in [[topological dynamics|5X6E97EMFR]].\n\n## Explanations\n\n### L1 human\n\nIn an equicontinuous system, if two starting points are close enough, their orbits remain close forever, and the needed closeness does not depend on how long one waits.\nRotating a circle is the model: it keeps all distances exactly.\nThe doubling map $x \\mapsto 2x \\bmod 1$ is not equicontinuous: two points at distance $\\delta$ move to distance $2\\delta$, then $4\\delta$, until they are far apart.\n",
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