Siegel disc

Summary

A Siegel disc is a component of the Fatou set of a rational map on which an iterate acts as an irrational rotation. The rotation is seen after a conformal change of coordinates. It surrounds a neutral periodic point whose multiplier is $e^{2\pi i \theta}$ with $\theta$ irrational. Whether such a disc exists depends on the arithmetic of $\theta$, through small divisor problems. Siegel discs are one of the four types of periodic Fatou components.