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• W3100555886 abstract "As a first step to understand how complicated attractors for dynamical systems can be, one may consider the following realizability problem: given a continuum $K subseteq mathbb{R}^3$, decide when $K$ can be realized as an attractor for a homeomorphism of $mathbb{R}^3$. In this paper we introduce toroidal sets as those continua $K subseteq mathbb{R}^3$ that have a neighbourhood basis comprised of solid tori and, generalizing the classical notion of genus of a knot, give a natural definition of the genus of toroidal sets and study some of its properties. Using these tools we exhibit knots and solenoids for which the answer to the realizability problem stated above is negative." @default.
• W3100555886 created "2020-11-23" @default.
• W3100555886 creator A5081411041 @default.
• W3100555886 creator A5089568284 @default.
• W3100555886 date "2019-12-05" @default.
• W3100555886 modified "2023-10-02" @default.
• W3100555886 title "Knots and Solenoids that Cannot Be Attractors of Self-homeomorphisms of ℝ3" @default.
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• W3100555886 doi "https://doi.org/10.1093/imrn/rnz251" @default.
• W3100555886 hasPublicationYear "2019" @default.
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