Comparison of tests for embeddings.
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.
Université de Rouen, CORIA UMR 6614, BP 12, F-76801 Saint-Etienne du Rouvray cedex, France.
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Letellier
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Moroz
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Gilmore