2014/08/03 by Han Peters, Peters, Han, Iris Marjan Smit +1 · 1 citation
Mathematics · Physics and Astronomy · #32H50 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #msc:32H50
paper · pdf · doi:10.48550/arxiv.1408.0498
34 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1311.3835
arxiv created 2014/08/03 · openalex publication_date 2014/08/03 · arxiv updated 2014/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a holomorphic automorphism acting hyperbolically on an invariant compact set. It has been conjectured that the arising stable manifolds are all biholomorphic to Euclidean space. Such a stable manifold is always equivalent to the basin of a uniformly attracting sequence of maps. The equivalence of such basins to Euclideans has been shown under various additional assumptions. Recently Majer and Abbondandolo achieved new results by non-autonomously conjugating to normal forms on larger and larger time intervals. We show here that their results can be improved by adapting these time intervals to the sequence of maps. Under the additional assumption that all maps have linear diagonal part the adaptation is quite natural and quickly leads to significant improvements. We show how this construction can be emulated in the non-diagonal setting.