Anisotropic properties of riddled basins
University of Exeter (at the time of publication Peter Ashwin was at the University of Surrey); University of Surrey
Physics Letters A
We consider some general properties of chaotic attractors with riddled basins of attraction (basins with positive measure but open dense complements) in dynamical systems with symmetries. We investigate how a basin of attraction can be riddled in some directions and not in others if the attractor is contained in the intersection of several invariant subspaces. This means that the extreme sensitivity to added noise (bubbling) associated with riddled basin attractors is in fact strongly dependent on the nature of the noise. We discuss examples of this for systems of globally coupled maps.
Copyright © 2001 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 Physics Letters A, Vol 280, Issue 3, 2001, DOI: 10.1016/S0375-9601(01)00043-3
280 (3), pp. 139-145