Perturbed Basins of Attraction

2004/11/15 by Han Peters, Peters, Han
Mathematics · Physics and Astronomy · #32H02 #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:32H02 #msc:32H50

paper · pdf · doi:10.48550/arxiv.math/0411339

11 pages

arxiv created 2004/11/15 · openalex publication_date 2004/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be an automorphism of C^k which has a fixed point. It is well known that the basin of attraction is biholomorphically equivalent to C^k. We will show that the basin of attraction of a sequence of automorphisms is also biholomorphic to C^k if all the automorphisms are small perturbations of the original map F.

Citations

• Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries

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• Examples of non-autonomous basins of attraction
• Remarks on Automorphisms of ℂ^* × ℂ^* and their basins
• Attracting basins of volume preserving automorphisms of ℂ^k