Escaping Fatou components with disjoint hyperbolic limit sets

2023/08/10 by Veronica Beltrami, Beltrami, Veronica, Anna Miriam Benini +3
Mathematics · #37F80 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2308.05529

openalex publication_date 2023/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct automorphisms of ℂ² with a cycle of escaping Fatou components, on which there are exactly two limit functions, both of rank 1. On each such Fatou component, the limit sets for these limit functions are two disjoint hyperbolic subsets of the line at infinity.

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