A useful canonical form for low dimensional attractors

Powerful computational techniques have been developed to study chaotic attractors that are generated by stretching and folding processes. These include relative rotation rates for determining the organization of unstable periodic orbits and simplex distortion procedures for estimating the topological entropy of these orbits. These methods are useful for attractors contained in a genus-one torus D × S, where all unstable orbits have a braid representation. We extend these methods to attractors in higher-genus tori (e.g., the Lorenz attractor) by mapping higher-genus attractors to diffeomorphic attractors that have a braid representation. We illustrate by computing the topological measures for orbits in the Lorenz attractor.