A note about Milnor attractor and riddled basin
type: Item
instance of: scholarly article
title: A note about Milnor attractor and riddled basin
zbMATH Open document ID: 1053.37012
DOI: 10.1016/S0960-0779(03)00205-4
published in: Chaos, Solitons and Fractals
publication date: 2004-07-01T00:00:00Z
review text: Attractors play an important role on the long-time behaviour of dynamical systems. In particular, a notion of an attractor was introduced by Milnor ignores initial conditions on a set of zero measure. This gives a theoretical framework for understanding attractors with ``riddled basin'' that are attracting for a large measure set of initial conditions. Here, the author presents some definitions and basic results on attractors. Moreover, the author gives some examples which show the relations between the Milnor attractor and the riddling attractor.
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 2077269
zbMATH Keywords: attractor
zbMATH Keywords: basin
zbMATH Keywords: Milnor attractor
zbMATH Keywords: initial data
zbMATH Keywords: measure zero
zbMATH Keywords: riddling attractor
author: Yongluo Cao
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: On riddling and weak attractors
cites work: The dynamics of the Hénon map
cites work: Solution of the basin problem for Hénon-like attractors
cites work: Strange attractor of Henon map and its basin
cites work: Strange attractors in the orientation-preserving Lozi map
cites work: Statistical properties of some almost hyperbolic systems
cites work: Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’
cites work: Quadratic maps without asymptotic measure
cites work: On the concept of attractor
cites work: VAK, vacuum fluctuation and the mass spectrum of high energy particle physics.
description: scientific article; zbMATH DE number 2077269