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Higher order Schwarzian derivatives in interval dynamics

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Kozlovski O., Sands D.

Fundamenta Mathematicae

2009

tom 206

nr 1

217-239

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Kozlovski O.

1 Sands D.

1 2009

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Higher order Schwarzian derivatives in interval dynamics