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Abstract In this paper we give a complete characterization of those knotted toroidal sets that can be realized as attractors for discrete or continuous dynamical systems globally defined in {R}³ R 3. We also see that the techniques used to solve this problem can be used to give sufficient conditions to ensure that a wide class of subcompacta of {R}³ R 3 that are attractors for homeomorphisms must also be attractors for flows. In addition we study certain attractor-repeller decompositions of {S}³ S 3 which arise naturally when considering toroidal sets.
Barge et al. (Mon,) studied this question.
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