2024/10/22 by Yuming Fu, Jun Hu, Fu, Yuming +3
Mathematics · #37F10 #Advanced Algebra and Geometry #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2410.16728
openalex publication_date 2024/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Under conjugation by affine transformations, the dynamical moduli space of cubic polynomials f with a 2-cycle of Siegel disks is parameterized by a three-punctured complex plane as a degree-2 cover. Assuming the rotation number of f2 on the Siegel disk is of bounded type, we show that on the three-punctured complex plane, the locus of the cubic polynomials with both finite critical points on the boundaries of the Siegel disks on the 2-cycle is comprised of two arcs, corresponding to the cases with two critical points on the boundary of the same Siegel disk, and a Jordan curve, corresponding to the cases with two critical points on the boundaries of different Siegel disks.