Distortion of S-unimodal maps
type: Item
instance of: scholarly article
title: Distortion of S-unimodal maps
zbMATH Open document ID: 0708.58007
DOI: 10.2307/1971501
author: John Guckenheimer
author: Stewart D. Johnson
published in: Annals of Mathematics. Second Series
publication date: 1990-01-01T00:00:00Z
review text: In the paper \(C^ 3\)-transformations f: \(I\to I\), \(I=[-1,1]\) are studied such that \(f(x)=h(x^ 2)\), h is monotone and has a negative Schwarzian derivative. Two categories of f are studied: (a) There is an attracting Cantor set that attracts almost every point and upon which f is homeomorphic or (b) the map is sensitive to initial conditions. It is proved that in case (a) all homeomorphic Cantor sets have Lebesgue measure zero, and in case (b) almost every point has the same \(\omega\)- limit set which is either finite union of intervals or an absorbing non- homeomorphic Cantor set.
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 34A40
zbMATH DE Number: 4163763
zbMATH Keywords: S-unimodal maps
zbMATH Keywords: Schwarzian derivative
reviewed by: Miroslav Bartušek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971501
OpenAlex ID: W2009131483
Wikidata QID: Q59541788
description: scientific article; zbMATH DE number 4163763