2022/12/30 by Héctor Barge, Barge, Héctor, J. J. Sánchez-Gabites +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2212.14642
openalex publication_date 2022/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℝ3. 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 ℝ3 that are attractors for homeomorphisms must also be attractors for flows. In addition we study certain attractor-repeller decompositions of \mathbbS3 which arise naturally when considering toroidal sets.