Lorenz attractors do not have the pseudo-orbit tracing property
type: Item
instance of: scholarly article
title: Lorenz attractors do not have the pseudo-orbit tracing property
zbMATH Open document ID: 0552.58020
author: Motomasa Komuro
published in: Journal of the Mathematical Society of Japan
publication date: 1985-01-01T00:00:00Z
review text: The paper investigates a pseudo-orbit tracing property (POTP) for a one- parameter flow on the geometric Lorenz attractor which is a modeled strange attractor of a flow on \(R^ 3\) defined by J. Guckenheimer. The main result is the following: (i) The geometric Lorenz attractors do not have the finite POTP, except a special case such that the return map f on [0,1] satisfies \(f(0)=0\) and \(f(1)=1\). (ii) The set of all vector fields whose flows satisfy the strong POTP is not dense in the space of all \(C^ 2\)-vector fields on a compact 3-manifold. This gives an answer of flow case for A. Morimoto's problem whether or not the set of all diffeomorphisms with POTP is dense in the space of all diffeomorphisms on a compact manifold.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 3879768
zbMATH Keywords: pseudo-orbit tracing property
zbMATH Keywords: Lorenz attractor
zbMATH Keywords: strange attractor
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03730489
OpenAlex ID: W1984832175
DOI: 10.2969/JMSJ/03730489
description: scientific article; zbMATH DE number 3879768