On riddling and weak attractors

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On riddling and weak attractors

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Terry, John R. en_GB
dc.date.accessioned 2008-03-19T15:11:11Z en_GB
dc.date.accessioned 2011-01-25T10:33:45Z en_US
dc.date.accessioned 2013-03-20T12:31:41Z
dc.date.issued 2000 en_GB
dc.description.abstract We propose general definitions for riddling and partial riddling of a subset V of Rm 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. en_GB
dc.identifier.citation 142 (1-2), pp. 87-100 en_GB
dc.identifier.doi 10.1016/S0167-2789(00)00062-2 en_GB
dc.identifier.uri http://hdl.handle.net/10036/21193 en_GB
dc.language.iso en en_GB
dc.publisher Elsevier en_GB
dc.relation.url http://dx.doi.org/10.1016/S0167-2789(00)00062-2 en_GB
dc.subject riddling en_GB
dc.subject riddled basin en_GB
dc.subject invariant manifold en_GB
dc.subject chaotic dynamical system en_GB
dc.subject Milnor attractor en_GB
dc.title On riddling and weak attractors en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-03-19T15:11:11Z en_GB
dc.date.available 2011-01-25T10:33:45Z en_US
dc.date.available 2013-03-20T12:31:41Z
dc.identifier.issn 0167-2789 en_GB
dc.description Copyright © 2000 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, Vol 142, Issues 1-2, 2000, DOI:10.1016/S0167-2789(00)00062-2 en_GB
dc.identifier.journal Physica D en_GB


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