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Published on: March 18, 2019
Dressed return maps distinguish chaotic mechanisms
1Physics Department, Haverford College, Haverford, Pennsylvania 19041, USA.
Abstract:
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.
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