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Embeddings of a strange attractor into R3.

The algorithm for determining a global Poincaré section is applied to a previously studied dynamical system on R2 x S1 and a one-parameter family of embeddings of the strange attractor it generates into R3. We find that the topological properties of the attractor are embedding dependent to a limited extent. These embeddings rigidly preserve mechanism, which is a simple stretch and fold. The embeddings studied show three discrete topological degrees of freedom: parity, global torsion, and braid type of the genus-one torus bounding the embedded attractor.