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On riddling and weak attractors
Terry, John R.
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.
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
142 (1-2), pp. 87-100