On the metric properties of multimodal interval maps and C2 density of Axiom A

• 成果类型: Article
• 署名作者: Shen, WX
• 署名单位: University of Warwick
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0343-2
• 发表日期: 2004
• 页码: 301-403
• 关键词: dimensional dynamical-systems; topological attractors; quadratic polynomials; wandering intervals; complex bounds; unimodal maps; sets; HYPERBOLICITY; nonexistence; geometry

摘要

In this paper, we shall prove that Axiom A maps are dense in the space of C-2 interval maps (endowed with the C-2 topology). As a step of the proof, we shall prove real and complex a priori bounds for (first return maps to certain small neighborhoods of the critical points of) real analytic multimodal interval maps with non-degenerate critical points. We shall also discuss rigidity for interval maps without large bounds.