Getting rid of the negative Schwarzian derivative condition

• 成果类型: Article
• 署名作者: Kozlovski, OS
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2661353
• 发表日期: 2000
• 页码: 743-762
• 关键词: one dimensional dynamics; HYPERBOLICITY; interval; MAPS

摘要

In this paper we will show that the assumption on the negative Schwarzian derivative is redundant in the case of C-3 unimodal maps with a nonflat critical point. The following theorem will be proved: For any C-3 unimodal map of an interval with a nonflat critical point there exists an interval around the critical value such that the first entry map to this interval has negative Schwarzian derivative. Another theorem proved in the paper provides useful cross-ratio estimates. Thus, all theorems proved only for unimodal maps with negative Schwarzian derivative can be easily generalized.