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Lissajous knots and billiard knots. (English) Zbl 0901.57012

Jones, Vaughan F. R. (ed.) et al., Knot theory. Proceedings of the mini-semester, Warsaw, Poland, July 13–August 17, 1995. Warszawa: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 42, 145-163 (1998).
Summary: The authors show that Lissajous knots are equivalent to billiard knots in a cube. They consider also knots in general 3-dimensional billiard tables. They analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
For the entire collection see [Zbl 0890.00048].

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry