Document Type

Journal Article

Role

Author

Standard Number

1539-3755

Journal Title

Physical Review E

Volume

87

Issue

1

First Page

012919

Last Page

012924

Publication Date

2013

Abstract

Chaotic data generated by a three-dimensional dynamical system can be embedded into R3 in a number of inequivalent ways. However, when lifted into R5 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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