Higher order Schwarzian derivatives in interval dynamics

• Autorzy: O. Kozlovski , D. Sands
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 41A20: Approximation by rational functions
• 30C20: Conformal mappings of special domains
• 53A55: Differential invariants (local theory), geometric objects
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 217-239

Daty

wydano

2009

Twórcy

autor

O. Kozlovski

• Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

autor

D. Sands

• CNRS, Département de Mathématiques, Université Paris-Sud, 91405 Orsay Cedex, France

Identyfikatory

DOI

10.4064/fm206-0-12