Harmonic Knots
Pierre-Vincent Koseleff (UPMC, IMJ, INRIA Paris-Rocquencourt), Daniel, Pecker (UPMC, IMJ)

TL;DR
This paper classifies harmonic knots parametrized by Chebyshev polynomials for small parameters, analyzing specific families and providing a comprehensive table of the simplest harmonic knots.
Contribution
It offers a classification of harmonic knots with small parameters and explores particular families, expanding understanding of their structure and properties.
Findings
Classified harmonic knots for a ≤ 4.
Analyzed knots of the form H(2n-1, 2n, 2n+1).
Provided a table of the simplest harmonic knots.
Abstract
The harmonic knot is parametrized as where , and are pairwise coprime integers and is the degree Chebyshev polynomial of the first kind. We classify the harmonic knots for We study the knots the knots and give a table of the simplest harmonic knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · semigroups and automata theory
