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  "body": "\n## Summary\n\nHolomorphic dynamics in several variables studies the iteration of holomorphic maps $f \\colon X \\to X$ of a [[complex manifold|JSGWAN2RJV]] $X$ of dimension at least $2$.\nThe two main families of examples are holomorphic endomorphisms of complex projective space $\\mathbb{P}^k$ and polynomial automorphisms of $\\C^2$, such as the [[Hénon maps|KS4FJ6H5JH]].\nAs in one-variable [[complex dynamics|BQQZ0ZCGQF]], space splits into a Fatou set, where the dynamics is stable, and a Julia set, where it is chaotic.\nMany tools are new, notably plurisubharmonic functions, positive closed currents and invariant measures.\n\n## Explanations\n\n### L1 human\n\nTake a holomorphic map of a space to itself and apply it again and again.\nEach starting point traces out an orbit, and the question is how these orbits behave.\nIn one complex variable this gives Julia sets and the Mandelbrot set.\nIn two or more variables the same question has richer answers: orbits can be attracted to curves, strange sets appear, and maps can be invertible yet chaotic.\nThe map $(x, y) \\mapsto (x^2 + c - y, x)$ of $\\C^2$ is a simple example: it is invertible, and its orbits already show this rich behaviour.\n",
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