Generating Dynamical Systems with Iterated Torus Knots as Solutions

The occurrence of knots as solutions of dynamical systems has been widely studied in the literature. In particular, ways to determine families of knots as solutions of differential equations have been described in several papers. In this article, an infinite family of dynamical systems, based on torus knots, is built each of which has the property that an infinite number of cable knots from torus knots (i.e., iterated torus knots) are obtained as solutions. One such dynamical system, based on the trefoil knot, is explicitly constructed. The methodology described herein may also be applied to any torus knot, and even to any other knot as long as a parametrization is provided for the latter. An example of application of the method is presented for the case of the figure eight knot, which is not a torus knot. Also, a possible application in cryptography is sketched.