Title: Topology of irrationally indifferent attractors,
Abstract: We study the attractors of a class of holomorphic systems with an
irrationally indifferent fixed point. We prove a trichotomy for the topology of
the attractor based on the arithmetic of the rotation number at the fixed
point. That is, the attractor is either a Jordan curve, a one-sided hairy
circle, or a Cantor bouquet. This has a number of remarkable corollaries on a
conjecture of M. Herman about the optimal arithmetic condition for the
existence of a critical point on the boundary of the Siegel disk, and a
conjecture of A. Douady on the topology of the boundary of Siegel disks.
Combined with earlier results on the topic, this completes the topological
description of the behaviors of typical orbits near such fixed points, when the
rotation number is of high type.