The Fatou Set for Critically Finite Maps

2006/08/19 by Feng Rong, Rong, Feng
Mathematics · Physics and Astronomy · #32H50 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #math.DS #msc:32H50

paper · pdf · doi:10.48550/arxiv.math/0608477

5 pages

arxiv created 2006/08/19 · openalex publication_date 2006/08/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is a classical result in complex dynamics of one variable that the Fatou set for a critically finite map on P¹ consists of only basins of attraction for superattracting periodic points. In this paper we deal with critically finite maps on P^k. We show that the Fatou set for a critically finite map on P² consists of only basins of attraction for superattracting periodic points. We also show that the Fatou set for a k-critically finite map on P^k is empty.

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