A two-dimensional polynomial mapping with a wandering Fatou component

• 成果类型: Article
• 署名作者: Astorg, Matthieu; Buff, Xavier; Dujardin, Romain; Peters, Han; Raissy, Jasmin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.184.1.2
• 发表日期: 2016
• 页码: 263-313
• 关键词: dimensional dynamical-systems; topological attractors; julia sets; nonexistence; intervals; Examples; domains; MAPS

摘要

We show that there exist polynomial endomorphisms of C-2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of P-2(C). We also find real examples with wandering domains in R-2. The proof is based on parabolic implosion techniques, and is based on an original idea of M. Lyubich.