Abstract
In [8] R.F. Williams showed that all knots in the Lorenz template are prime. His proof included the cases where any number of positive twists were added to one of the template’s branches. However [8] does give an example of a composite knot in a template with a single negative twist. Below we will show that in all the negative cases composite knots do exist, and give a mechanism for producing many examples. This problem was cited in a list of problems in dynamics in [1, problem 4.2].
Comments
Electronic version, with some figures missing, of an article published as "Prime Decomposition of Knots in Lorenz-like Templates," Journal of Knot Theory and Its Ramifications, 2(4), 1993, 453 - 462. DOI: 10.1142/S021821659300026X © copyright World Scientific Publishing Company, http://www.worldscinet.com/jktr/