Letellier, C. and Moroz, I. M. and Gilmore, R. (2008) A Comparison of Tests for Embeddings. Phys. Rev E, 78 .
Official URL: http://link.aps.org/abstract/PRE/v78/e026203
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.
|Uncontrolled Keywords:||Dynamical Systems; Embeddings|
|Subjects:||D - G > Dynamical systems and ergodic theory|
|Research Groups:||Mathematical Geoscience Group|
Oxford Centre for Industrial and Applied Mathematics
|Deposited By:||Irene Moroz|
|Deposited On:||23 Oct 2008|
|Last Modified:||20 Jul 2009 15:06|
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