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Quadratic rational maps with a $2$-cycle of Siegel disks
- Publication Year :
- 2020
-
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.<br />Comment: 21 pages, 7 figures; to appear in the Journal of Geometric Analysis
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2012.10818
- Document Type :
- Working Paper