Chebyshev Knots
Abstract
A Chebyshev knot is a knot which admits a parametrization of the form x(t)=Ta(t); \ y(t)=Tb(t) ; \ z(t)= Tc(t + φ), where a,b,c are pairwise coprime, Tn(t) is the Chebyshev polynomial of degree n, and φ ∈ . Chebyshev knots are non compact analogues of the classical Lissajous knots. We show that there are infinitely many Chebyshev knots with φ = 0. We also show that every knot is a Chebyshev knot.
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