Chebyshev Knots

Details Chebyshev Knots Chebyshev Knots

2008-12-05

arxiv.org/abs/0812.1089v2

Mathematics

Geometric Topology

To appear in Journal of Knot Theory and Ramifications

Scientific paper

A Chebyshev knot is a knot which admits a parametrization of the form $ x(t)=T_a(t); \ y(t)=T_b(t) ; \ z(t)= T_c(t + \phi), $ where $a,b,c$ are pairwise coprime, $T_n(t)$ is the Chebyshev polynomial of degree $n,$ and $\phi \in \RR .$ Chebyshev knots are non compact analogues of the classical Lissajous knots. We show that there are infinitely many Chebyshev knots with $\phi = 0.$ We also show that every knot is a Chebyshev knot.

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