A polynomial automorphism with a wandering Fatou component

2018/07/06 by David W. Hahn, Hahn, David, Han Peters +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · doi:10.48550/arxiv.1807.02466

openalex publication_date 2018/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct polynomial automorphisms with wandering Fatou components. The four-dimensional automorphisms H lie in a one-parameter family, depending on the parameter δ∈ \mathbb C ∖ \0\, and as δ→ 0 the automorphisms degenerate to the two-dimensional polynomial map P constructed in Astorg et al (Ann. of Math., 2016). Our main result states that if P has a wandering domain, then H does too for δ sufficiently small.

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