Attracting sequences of holomorphic automorphisms that agree to a certain order

2017/02/25 by Rafael B. Andrist, Andrist, Rafael B., Gerrit W. Maus +1
Mathematics · #32H02 #32H50 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1702.07953

openalex publication_date 2017/02/25 · openalex created_date 2017/03/16 · openalex updated_date 2026/07/28

Abstract

The basin of attraction of a uniformly attracting sequence of holomorphic automorphisms that agree to a certain order in the common fixed point, is biholomorphic to ℂⁿ. We also give sufficient estimates how large this order has to be.

Related

• Perturbed Basins of Attraction
• Uniform non-autonomous basins of attraction
• Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries
• Attracting basins of volume preserving automorphisms of ℂ^k
• Automorphisms of \mathbb C^k with an invariant non-recurrent attracting Fatou component biholomorphic to \mathbb C× (\mathbb C^∗)^k-1