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Real bounds, ergodicity and negative Schwarzian for multimodal maps
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Strien, Sebastian van and Vargas, Edson (2007) Real bounds, ergodicity and negative Schwarzian for multimodal maps. Journal of the American Mathematical Society, Volume 20 (Number 1). pp. 267-268. ISSN 1088-6834 doi:10.1090/S0894-0347-06-00535-2
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Official URL: http://www.ams.org/journals/jams/2004-17-04/S0894-...
Abstract
We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful improved Koebe principles, show that high iterates have `negative Schwarzian derivative' and give results on ergodic properties of the map. One of the main complications in the proofs is that we allow to have inflection points.
Item Type: | Journal Item | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 1088-6834 | ||||
Official Date: | 27 August 2007 | ||||
Dates: |
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Volume: | Volume 20 | ||||
Number: | Number 1 | ||||
Number of Pages: | 2 | ||||
Page Range: | pp. 267-268 | ||||
DOI: | 10.1090/S0894-0347-06-00535-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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