Links and Dynamics Full article
| Journal |
Russian Journal of Nonlinear Dynamics
ISSN: 2658-5324 , E-ISSN: 2658-5316 |
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| Output data | Year: 2025, Volume: 21, Number: 1, Pages: 69–83 Pages count : 15 DOI: 10.20537/nd241004 | ||||||||||
| Tags | knot, link, equivalence class of links, braid, mixed braid, fundamental quandle, handlebody, 3-manifold | ||||||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | 075-02-2024-1437 |
Abstract:
Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and links. For example, for Pixton diffeomorphisms, the equivalence class of the Hopf knot, which is the orbit space of the unstable saddle separatrix in the manifold S2×S1, is a complete invariant of the topological conjugacy of the system. In this paper we distinguish a class of three-dimensional Morse--Smale diffeomorphisms for which the complete invariant of topological conjugacy is the equivalence class of a link in S2×S1. We prove that if M is a link complement in S3, or a handlebody Hg of genus g≥0, or a closed, connected, orientable 3-manifold, then the set of equivalence classes of tame links in M is countable. As a corollary, we prove that there exists a countable number of equivalence classes of tame links in S2×S1. It is proved that any essential link can be realized by a diffeomorphism of the class under consideration.
Cite:
Bardakov V.G.
, Kozlovskaya T.A.
, Pochinka O.V.
Links and Dynamics
Russian Journal of Nonlinear Dynamics. 2025. V.21. N1. P.69–83. DOI: 10.20537/nd241004 Scopus РИНЦ OpenAlex
Links and Dynamics
Russian Journal of Nonlinear Dynamics. 2025. V.21. N1. P.69–83. DOI: 10.20537/nd241004 Scopus РИНЦ OpenAlex
Dates:
| Submitted: | May 16, 2024 |
| Accepted: | Aug 7, 2024 |
| Published print: | Apr 28, 2025 |
| Published online: | Apr 28, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105002439886 |
| Elibrary: | 81021680 |
| OpenAlex: | W4403406618 |
Citing:
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