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Studying attractor symmetries by means of cross-correlation sums

We use the cross-correlation sum introduced recently by Kantz to study symmetry properties of chaotic attractors or, more precisely, of invariant measures supported by such attractors. In particular, we apply it to a system of six coupled nonlinear oscillators which was shown by Kroon et al to have attractors with several different symmetries, and compare our results with those obtained by `detectives' in the sense of Golubitsky et al.