Decay of geometry for unimodal maps: An elementary proof

• 成果类型: Article
• 署名作者: Shen, Weixiao
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.383
• 发表日期: 2006
• 页码: 383-404
• 关键词: quadratic polynomials; induced expansion; metric properties; DYNAMICS; attractors; sets

摘要

We prove that a nonrenormalizable smooth unimodal interval map with critical order between 1 and 2 displays decay of geometry, by an elementary and purely real argument. This completes a real approach to Milnor's attractor problem for smooth unimodal maps with critical order not greater than 2.