1994/12/19 by Kevin M. Pilgrim, Pilgrim, Kevin M.
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.math/9412205
Separate uu-encoded "tar" file of figures sent also. Uses Latex2.09 and geompsfi.sty
arxiv created 1994/12/19 · openalex publication_date 1994/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove: If f(z) is a critically finite rational map which has exactly two critical points and which is not conjugate to a polynomial, then the boundary of every Fatou component of f is a Jordan curve. If f(z) is a hyperbolic critically finite rational map all of whose postcritical points are periodic, then there exists a cycle of Fatou components whose boundaries are Jordan curves. We give examples of critically finite hyperbolic rational maps f with the property that on the closure of a Fatou component Ω satisfying f(Ω)=Ω, f|\bdry Ω is not topologically conjugate to the dynamics of any polynomial on its Julia set.