Phys. Rev. E 78, 026203 (2008) [11 pages]Comparison of tests for embeddingsReceived 17 December 2007; published 6 August 2008 It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions. © 2008 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.78.026203
DOI:
10.1103/PhysRevE.78.026203
PACS:
05.45.−a
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