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  "body": "\n## Definition\n\nLet $f \\colon \\hat{\\C} \\to \\hat{\\C}$ be a [[rational function|0XDK9CGYKJ]] of degree at least $2$ on the [[Riemann sphere|0J78KBPFZB]] $\\hat{\\C}$.\nLet $F(f)$ be the [[Fatou set|C0N0XGC6GK]] of $f$.\nThe *Julia set* of $f$ is the complement $J(f) = \\hat{\\C} \\setminus F(f)$.\nSo a point $z$ lies in $J(f)$ if and only if the iterates $f^n$, $n \\ge 0$, form a normal family on no open neighbourhood of $z$.\n\n## Remarks\n\nExample: for $f(z) = z^2$, $J(f)$ is the unit circle.\nOn $\\abs{z} \u003c 1$ the iterates $z^{2^n}$ tend to $0$ locally uniformly, and on $\\abs{z} \u003e 1$ they tend to $\\infty$, so both regions lie in $F(f)$.\nEvery neighbourhood of a point with $\\abs{z} = 1$ contains points whose orbits tend to $0$ and points whose orbits tend to $\\infty$.\nSo a limit of a subsequence of iterates would be discontinuous there, and the point is in $J(f)$.\nNon-example: $z = 1/2$ is not in $J(z^2)$, because the disc $\\abs{z} \u003c 3/4$ lies in the Fatou set.\nFor degree at least $2$, $J(f)$ is nonempty, compact and perfect, it satisfies $f^{-1}(J(f)) = J(f)$, and it is the closure of the set of repelling periodic points.\nThe same definition, with $\\C$ in place of $\\hat{\\C}$, is used for transcendental entire functions.\n",
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