Attractors from one dimensional Lorenz-like maps
type: Item
instance of: scholarly article
title: Attractors from one dimensional Lorenz-like maps
zbMATH Open document ID: 1065.37028
author: Youngna Choi
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-10-27T00:00:00Z
review text: The author studies a collection of functions with following properties: (i) \(f: [a,b]\to [a,b]\); (ii) \(f\) has a jump discontinuity at a fixed-point \(c\in (a,b)\); (iii) \(f\) is \(C^1\) on \([a,b]\setminus\{c\}\) and there is a number \(\lambda> 1\) such that \(|f'(x)|> \lambda\) whenever \(f'(x)\) exists. Then there exists a compact invariant set \(L_f\subset [a,b]\), \(c\in L_f\), such that the restriction \(f|L_f\) is topologically transitive and \(W^s(L_f)= \{x\in [a,b]: f^n(x)\to L_f\}\) is open and dense. The author investigates the structure of the set \(L_f\) and gives an explicit construction of a trapping region \(N\) for \(L_f\). Finally, the properties, which are persistent with respect to continuous perturbations of \(f\), are investigated.
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37G35
Mathematics Subject Classification ID: 37D20
zbMATH DE Number: 2110784
zbMATH Keywords: expanding maps
zbMATH Keywords: invariant sets
zbMATH Keywords: attractors
zbMATH Keywords: trapping region
zbMATH Keywords: perturbation
reviewed by: A. Klíč
MaRDI profile type: Publication
full work available at URL: dcds.2004.11.715
OpenAlex ID: W2090410123
DOI: 10.3934/DCDS.2004.11.715
Recommended article: Lorenz type attractors from codimension one bifurcation
Recommended article: Periodic attractors of perturbed one-dimensional~maps
Recommended article: Attractors for one kind of lattice dynamical system
Recommended article: Attractors in a Šil'nikov-Hopf scenario and a related one-dimensional map
Recommended article: Attracteurs de Lorenz de variété instable de dimension arbitraire
Recommended article: Q4762734
Recommended article: Cyclicity of chaotic attractors in one-dimensional discontinuous maps
Recommended article: Q4313511
Recommended article: Bifurcations of Chaotic Attractors in One-Dimensional Piecewise Smooth Maps
Recommended article: Q3499811
description: scientific article; zbMATH DE number 2110784