 Siegel disc

A Siegel disc is a simply connected periodic Fatou component on which the first-return map is holomorphically conjugate to an irrational rotation of the unit disc: $h\circ R^p\circ h^{-1}(w)=e^{2\pi i\theta }w$, with $\theta \notin \mathbb{Q}$. Its return iterates are normal because any sequence of rotation factors has a convergent subsequence in the unit circle, giving locally uniform limits after conjugation. The iterates generally do not converge to a constant. This is a rotation domain, illustrating stability without attraction.

A Siegel disc is a concept in complex dynamics, a branch of mathematics that studies the behavior of iterated functions in the complex plane. It is associated with the dynamics of certain types of complex functions, particularly polynomial maps.