Higher order Schwarzian derivatives in interval dynamics

O. Kozlovski, and D. Sands. "Higher order Schwarzian derivatives in interval dynamics." Fundamenta Mathematicae 206.1 (2009): 217-239. <http://eudml.org/doc/283229>.

@article{O2009,
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 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.},
author = {O. Kozlovski, D. Sands},
journal = {Fundamenta Mathematicae},
keywords = {interval dynamics; Schwarzian derivative; rational approximation; Pick class},
language = {eng},
number = {1},
pages = {217-239},
title = {Higher order Schwarzian derivatives in interval dynamics},
url = {http://eudml.org/doc/283229},
volume = {206},
year = {2009},
}

TY - JOUR
AU - O. Kozlovski
AU - D. Sands
TI - Higher order Schwarzian derivatives in interval dynamics
JO - Fundamenta Mathematicae
PY - 2009
VL - 206
IS - 1
SP - 217
EP - 239
AB - 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.
LA - eng
KW - interval dynamics; Schwarzian derivative; rational approximation; Pick class
UR - http://eudml.org/doc/283229
ER -