Uniform non-autonomous basins of attraction

• 成果类型: Article
• 署名作者: Bera, Sayani; Verma, Kaushal
• 署名单位: Department of Science & Technology (India); Indian Association for the Cultivation of Science (IACS) - Jadavpur; Indian Institute of Science (IISC) - Bangalore
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01295-9
• 发表日期: 2024
• 页码: 995-1040
• 关键词: polynomial automorphisms; stable manifolds

摘要

It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be biholomorphic to the basin of a uniformly attracting family of holomorphic maps. It is shown that the basin of a uniformly attracting family of holomorphic maps is biholomorphic to complex Euclidean space and this resolves the conjecture on the biholomorphism type of such stable manifolds affirmatively.