The Mathematical Institute, University of Oxford, Eprints Archive

A Comparison of Tests for Embeddings

Letellier, C. and Moroz, I. M. and Gilmore, R. (2008) A Comparison of Tests for Embeddings. Phys. Rev E, 78 .

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Official URL: http://link.aps.org/abstract/PRE/v78/e026203

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 the reasons for this failure, which are not restricted to three dimensions.

Item Type:Article
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
ID Code:746
Deposited By:Irene Moroz
Deposited On:23 Oct 2008
Last Modified:20 Jul 2009 15:06

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