Abstract
In [Spears et al., 2005] it was demonstrated that insight into the geometry and topology of attractors for nonlinear oscillators driven by n incommensurate frequencies may be obtained from the study of n Poincaré maps defined on global cross-sections. The attractors take the form of stable torus braids. Here, attention is focused on saddle-type torus braids in similar systems. Transverse intersections of stable and unstable manifolds are computed using the phase slice method, along with the application of the crossover map. This neatly maps from one global Poincaré section to another. As such, it can be used to compute lobe intersection geometries in the remaining n - 1 Poincaré sections after doing so by the phase slice method in the first.
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