The realization problem of non-connected compacta as attractors

Barge, Héctor; Sánchez-Gabites, J. J.

doi:10.1016/j.topol.2023.108573

Topology and its Applications

2023

DOI: 10.1016/j.topol.2023.108573

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The realization problem of non-connected compacta as attractors

Héctor Barge

J. J. Sánchez-Gabites

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2024

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Knotted toroidal sets, attractors and incompressible surfaces

Barge,

Sánchez-Gabites

2024

Sel. Math. New Ser.

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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 $${\mathbb {R}}^3$$ 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.

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Knotted toroidal sets, attractors and incompressible surfaces

Barge,

Sánchez-Gabites

2024

Sel. Math. New Ser.

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The realization problem of non-connected compacta as attractors

Cited by 1 publication

References 27 publications

Knotted toroidal sets, attractors and incompressible surfaces

Knotted toroidal sets, attractors and incompressible surfaces

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