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  "body": "\n## Summary\n\nA Siegel disc is a component of the [[Fatou set|C0N0XGC6GK]] of a rational map on which an iterate acts as an irrational rotation.\nThe rotation is seen after a conformal change of coordinates.\nIt surrounds a neutral periodic point whose multiplier is $e^{2\\pi i \\theta}$ with $\\theta$ irrational.\nWhether such a disc exists depends on the arithmetic of $\\theta$, through small divisor problems.\nSiegel discs are one of the four types of periodic Fatou components.\n\n## Explanations\n\n### L1 human\n\nImagine a disc that the map turns by a fixed angle at each step, like a wheel.\nThe angle is an irrational fraction of a full turn, so no point ever returns exactly to where it started.\nEach point travels forever along a closed curve around a centre point.\nFor $z \\mapsto e^{2\\pi i \\theta} z + z^2$ with $\\theta$ the golden mean, such a turning disc exists around $0$.\nIts boundary is a complicated fractal curve.\n",
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