CHEBYSHEV KNOTS-Reference-Cited by-同舟云学术

CHEBYSHEV KNOTS

Published:2011-04 Issue:04 Volume:20 Page:575-593
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

KOSELEFF P.-V.¹,PECKER D.²

Affiliation:

1. Université Pierre et Marie Curie, INRIA-Paris-Rocquencourt Salsa, and Laboratoire d'Informatique de Paris 6, CNRS (UMR 7606) 4, Place Jussieu, F-75252 Paris Cedex 05, France

2. Université Pierre et Marie Curie, 4, Place Jussieu, F-75252 Paris Cedex 05, France

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 integers, Tn(t) is the Chebyshev polynomial of degree n, and φ ∈ R. 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216511009364

Reference23 articles.

1. Annals of Mathematics Studies;Birman J. S.,1974

2. LISSAJOUS KNOTS

3. Sampling Lissajous and Fourier Knots

4. Plane Algebraic Curves

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