Dressed return maps distinguish chaotic mechanisms

Chaotic data generated by a three-dimensional dynamical system can be embedded into R(3) in a number of inequivalent ways. However, when lifted into R(5) they all become equivalent, indicating that they all belong to a single universality class sharing a common chaos-generating mechanism. We present a complete invariant determining this universality class and distinguishing attractors generated by distinct mechanisms. This invariant is easily computable from an appropriately "dressed" return map of any particular three-dimensional embedding.