Higher order Schwarzian derivatives in interval dynamics

Details Higher order Schwarzian derivatives in interval dynamics Higher order Schwarzian derivatives in interval dynamics

2008-12-14

arxiv.org/abs/0812.2646v1

Mathematics

Dynamical Systems

21 pages

Scientific paper

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.

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