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  "body": "\n## Summary\n\nBerkovich space dynamics studies the iteration of a rational map over a complete non-Archimedean field on the Berkovich projective line.\nMore generally, it studies endomorphisms of Berkovich analytic spaces.\nThe field itself, such as $\\C_p$, is totally disconnected and not locally compact, which makes analysis of orbits awkward.\nThe Berkovich projective line adds extra points to $\\mathbb{P}^1(\\C_p)$ and is compact, Hausdorff and path-connected.\nEvery rational map extends to it continuously.\nOn this space one gets [[Julia sets|5M4S7P04GR]], [[Fatou sets|C0N0XGC6GK]] and invariant measures that behave much like those of [[complex dynamics|BQQZ0ZCGQF]].\n\n## Explanations\n\n### L1 human\n\nOver the $p$-adic numbers, discs never overlap partially and the space falls apart into tiny pieces.\nBerkovich added one new point for each closed disc, together with a few limit points, so that the discs are joined together into a tree-like space.\nA rational map moves discs to discs, so it moves these new points too.\nFor the map $z \\mapsto z^2$, the point that stands for the closed unit disc stays fixed.\nThis point is the whole Julia set, while on the ordinary $p$-adic points the Julia set is empty.\n",
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