Generic family with robustly infinitely many sinks

• 成果类型: Article
• 署名作者: Berger, Pierre
• 署名单位: Universite Paris 13
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0632-6
• 发表日期: 2016
• 页码: 121-172
• 关键词: surface diffeomorphisms; homoclinic tangency; global perspective; DYNAMICS; HYPERBOLICITY; MAPS; dimensions; attractors; sets

摘要

We show, for every or , the existence of a Baire generic set of -families of -maps of a manifold M of dimension 2, so that for every a small the map has infinitely many sinks. When the dimension of the manifold is 3, the generic set is formed by families of diffeomorphisms. When M is the annulus, this generic set is formed by local diffeomorphisms. This is a counter example to a conjecture of Pugh and Shub.