Comparison of tests for embeddings.

Author: 

Letellier, C
Moroz, I
Gilmore, R

Publication Date: 

August 2008

Journal: 

Phys Rev E Stat Nonlin Soft Matter Phys

Last Updated: 

2019-04-27T22:20:03.233+01:00

Issue: 

2 Pt 2

Volume: 

78

DOI: 

10.1103/PhysRevE.78.026203

page: 

026203-

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.

Symplectic id: 

5370

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article