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  "body": "\n## Summary\n\n$p$-adic dynamics studies the iteration of maps defined over the [[$p$-adic numbers|BT6T702C28]] and their extensions, such as rational functions and convergent power series.\nIt is a [[discrete-time dynamical system|5AA9AJEARJ]] theory in which distances come from a [[non-Archimedean absolute value|1H5F1BP6XS]].\nThe strong triangle inequality makes the behaviour of orbits very different from the real or complex case.\nIt is a basic tool of [[arithmetic dynamics|BE4X0QG8XW]], where $p$-adic methods control orbits of points over number fields.\n\n## Explanations\n\n### L1 human\n\nIn $p$-adic numbers two numbers are close when their difference is divisible by a high power of $p$.\nIterating a map in this world means following a point step by step and watching how its $p$-adic size changes.\nDiscs either nest inside each other or do not meet, so orbits often move in very rigid patterns.\nFor example, the map $x \\mapsto x + 1$ on the $p$-adic integers sends $0$ to $1, 2, 3, \\dots$, and these points come arbitrarily close to every $p$-adic integer.\n",
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