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Journal Articles Journal of Knot Theory and Its Ramifications Year : 2011

Chebyshev Knots


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 $\phi \in \mathbb{R} .$ 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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Dates and versions

hal-00344501 , version 1 (04-12-2008)
hal-00344501 , version 2 (08-04-2010)



Pierre-Vincent Koseleff, Daniel Pecker. Chebyshev Knots. Journal of Knot Theory and Its Ramifications, 2011, 20 (4), pp.575-593. ⟨10.1142/S0218216511009364⟩. ⟨hal-00344501v2⟩
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