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A Comparison of Tests for Embeddings

Abstract:

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...

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Publication date:
2008-08-06
URN:
uuid:34c35280-6cd6-4e77-bde1-bf6f2b004530
Local pid:
oai:eprints.maths.ox.ac.uk:746

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