Quadratic rational maps with a 2-cycle of Siegel disks

2020/12/20 by Yuming Fu, Fei Yang, Fu, Yuming +3
Mathematics · #Mathematical Dynamics and Fractals #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2012.10818

Abstract

For the family of quadratic rational functions having a 2-cycle of bounded type Siegel disks, we prove that each of the boundaries of these Siegel disks contains at most one critical point. In the parameter plane, we prove that the locus for which the boundaries of the 2-cycle of Siegel disks contain two critical points is a Jordan curve.

Related

• Quadratic Siegel Disks with Rough Boundaries
• The high type quadratic Siegel disks are Jordan domains
• Dynamics of Siegel Rational Maps with Prescribed Combinatorics
• Polynomial Siegel disks are typically Jordan domains
• All bounded type Siegel disks of rational maps are quasi-disks