On riddling and weak attractors

被引:36
作者
Ashwin, P [1 ]
Terry, JR [1 ]
机构
[1] Univ Surrey, Dept Math & Stat, Guildford GU2 5XH, Surrey, England
基金
英国工程与自然科学研究理事会;
关键词
riddling; riddled basin; invariant manifold; chaotic dynamical system; Milnor attractor;
D O I
10.1016/S0167-2789(00)00062-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We propose general definitions for riddling and partial riddling of a subset V of R-m with non-zero Lebesgue measure and show that these properties are invariant for a large class of dynamical systems. We introduce the concept of a weak attractor, a weaker notion than a Milnor attractor and use this to re-examine and classify riddled basins of attractors. We find that basins of attraction can be partially riddled but if this is the case then any partial riddling must be evident near the attractor. We use these concepts to aid classification of bifurcations of attractors from invariant subspaces. In particular, our weak attractor is a generalisation of the absorbing area investigated by other authors and we suggest that a transition of a basin to riddling is usually associated with loss of stability of a weak attractor. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:87 / 100
页数:14
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