Author:
Barge Héctor,Sánchez-Gabites J. J.
Abstract
AbstractIn 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 $${\mathbb {R}}^3$$
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 $${\mathbb {R}}^3$$
R
3
that are attractors for homeomorphisms must also be attractors for flows. In addition we study certain attractor-repeller decompositions of $${\mathbb {S}}^3$$
S
3
which arise naturally when considering toroidal sets.
Funder
Universidad Politécnica de Madrid
Publisher
Springer Science and Business Media LLC
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