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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.
Research output not available from this repository, contact author.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: |
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| Volume: | 152 | ||||
| Number: | 3 | ||||
| Number of Pages: | 20 | ||||
| Page Range: | pp. 743-762 | ||||
| Publication Status: | Published |
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