Classifying 3-trip Lorenz knots (Q1064614)
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scientific article; zbMATH DE number 3921533
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classifying 3-trip Lorenz knots |
scientific article; zbMATH DE number 3921533 |
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Classifying 3-trip Lorenz knots (English)
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1985
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The paper is concerned with a problem treated in [\textit{J. Birman} and \textit{R. Williams}, Topology 22, 47-82 (1983; Zbl 0507.58038)] where knotted orbits in \(S^ 3\) of a certain system of linear differential equations (Lorenz equations) were studied. The occurring knots and links were classified up to a certain complexity (trip number \(\leq 2)\). The author here classifies those of trip number 3. Using the representation of 3-trip (Lorenz-) knots as closed 3-bridges an explicit enumeration of those knots is given. The classification makes use of the Alexander polynomials.
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strange attractors
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closed braids
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knotted orbits of a system of
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linear differential equations
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Lorenz equations
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trip number
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Alexander polynomials
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