More on knots in Robinson's attractor

Abstract

In an earlier paper the second author made a study of the knotted periodic orbits in a strange attractor for a set of differential equations in a paper by Clark Robinson. The attractor is modeled by a Lorenz-like template. It was shown that the knots and links are positive but need not be positive braids. Here we show that they are fibered, have positive signature, and that each knot-type appears infinitely often. We then construct a zeta type function that counts periodic orbits by the twisting of the local stable manifolds.