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arXiv · 2212.14642

Knotted toroidal sets, attractors and incompressible surfaces

Héctor Barge·J. J. Sánchez-Gabites
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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 both discrete and continuous dynamical systems globally defined in $\mathbb{R}^3$. 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 $\mathbb{R}^3$ that are attractors for homeomorphisms must also be attractors for flows. In addition we study certain attractor-repeller decompositions of $\mathbb{S}^3$ which arise naturally when considering toroidal sets.

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Héctor Barge, J. J. Sánchez-Gabites. 2022-12-30. Knotted toroidal sets, attractors and incompressible surfaces. https://arxiv.org/abs/2212.14642

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