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Getting rid of the negative Schwarzian derivative condition

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UNSPECIFIED (2000) Getting rid of the negative Schwarzian derivative condition. ANNALS OF MATHEMATICS, 152 (3). pp. 743-762.

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Abstract

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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Journal or Publication Title: ANNALS OF MATHEMATICS
Publisher: ANN MATHEMATICS
ISSN: 0003-486X
Official Date: November 2000
Dates:
DateEvent
November 2000UNSPECIFIED
Volume: 152
Number: 3
Number of Pages: 20
Page Range: pp. 743-762
Publication Status: Published

Data sourced from Thomson Reuters' Web of Knowledge

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