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Higher order Schwarzian derivatives in interval dynamics
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Kozlovski, O. and Sands, D. (2009) Higher order Schwarzian derivatives in interval dynamics. In: International Conference on Dynamical Systems held in honor of Michal Misurewicz, Polish Acad Sci, Inst Math, Bedlewo, Poland, 2008. Published in: Fundamenta Mathematicae, Vol.206 pp. 217-239. doi:10.4064/fm206-0-12 ISSN 0016-2736.
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Official URL: http://dx.doi.org/10.4064/fm206-0-12
Abstract
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives tip to some order, obtaining control over derivatives of high order. For a large class of multimodal interval maps we show that all inverse branches of first return naps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives positive tip to any given order.
Item Type: | Conference Item (Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Fundamenta Mathematicae | ||||
Publisher: | Polska Akademia Nauk | ||||
ISSN: | 0016-2736 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.206 | ||||
Number of Pages: | 23 | ||||
Page Range: | pp. 217-239 | ||||
DOI: | 10.4064/fm206-0-12 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | International Conference on Dynamical Systems held in honor of Michal Misurewicz | ||||
Type of Event: | Conference | ||||
Location of Event: | Polish Acad Sci, Inst Math, Bedlewo, Poland | ||||
Date(s) of Event: | 2008 |
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