All Bounded Type Siegel Disks of Rational Maps Are Quasi-disks
نویسنده
چکیده
We prove that every bounded type Siegel disk of a rational map must be a quasi-disk with at least one critical point on its boundary. This verifies Douady-Sullivan’s conjecture in the case of bounded type rotation numbers.
منابع مشابه
Dynamics of Siegel Rational Maps with Prescribed Combinatorics
We extend Thurston’s combinatorial criterion for postcritically finite rational maps to a class of rational maps with bounded type Siegel disks. The combinatorial characterization of this class of Siegel rational maps plays a special role in the study of general Siegel rational maps. As one of the applications, we prove that for any quadratic rational map with a bounded type Siegel disk, the bo...
متن کاملIs the Boundary of a Siegel Disk a Jordan Curve?
Bounded irreducible local Siegel disks include classical Siegel disks of polynomials, bounded irreducible Siegel disks of rational and entire functions, and the examples of Herman and Moeckel. We show that there are only two possibilities for the structure of the boundary of such a disk: either the boundary admits a nice decomposition onto a circle, or it is an indecomposable continuum.
متن کاملOn Siegel Disks of a Class of Entire Maps
Let f : C → C be an entire map of the form f(z) = P (z) exp(Q(z)), where P and Q are polynomials of arbitrary degrees (we allow the case Q = 0). Building upon a method pioneered by M. Shishikura, we show that if f has a Siegel disk of bounded type rotation number centered at the origin, then the boundary of this Siegel disk is a quasicircle containing at least one critical point of f . This uni...
متن کاملAutomorphisms of Rational Manifolds of Positive Entropy with Siegel Disks
Using McMullen’s rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk.
متن کاملSemi-continuity of Siegel Disks under Parabolic Implosion
We transfer the lower semi-continuity of Siegel disks with fixed Brjuno type rotation numbers to geometric limits. Here, we restrict to Lavaurs maps associated to quadratic polynomials with a parabolic fixed point.
متن کامل