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  "body": "\n## Summary\n\nA periodic point of a map is a point that comes back to itself after some positive number of steps.\nIts orbit is a finite cycle that repeats forever.\n[[Fixed points|R6QVS6P21N]] are the periodic points that return after one step.\nPeriodic points are the simplest kind of long-time behaviour, and counting them says a lot about a system.\nFor flows the analogue is a [[periodic orbit|0AA97XA70K]].\n\n## Explanations\n\n### L1 human\n\nStart at a point, apply the map again and again, and watch whether the point ever comes back.\nIf it comes back after $n$ steps, it will repeat the same loop of $n$ points forever.\nFor $f(x) = -x$ on the real line, the point $1$ goes to $-1$ and then back to $1$, so it is periodic with period $2$.\nFor the rotation of a clock face by one hour, every point comes back after $12$ steps.\n",
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