Higher order Schwarzian derivatives in interval dynamics
O. Kozlovski ; D. Sands
Fundamenta Mathematicae, Tome 205 (2009), p. 217-239 / Harvested from The Polish Digital Mathematics Library

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 up 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 maps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives positive up to any given order.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:283229
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     author = {O. Kozlovski and D. Sands},
     title = {Higher order Schwarzian derivatives in interval dynamics},
     journal = {Fundamenta Mathematicae},
     volume = {205},
     year = {2009},
     pages = {217-239},
     zbl = {1187.37055},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-12}
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O. Kozlovski; D. Sands. Higher order Schwarzian derivatives in interval dynamics. Fundamenta Mathematicae, Tome 205 (2009) pp. 217-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-12/